How do Biblical Unitarians understand what some theologians refer as the Kenosis in Philippians 2?

Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross. Therefore God has highly exalted him and bestowed on him the name that is above every name...

There is little complexity here so long as one reading does not superimpose presupposed beliefs onto the text.

The imposition of an alleged time-frame for the various details is a distraction and unwarranted by the text.

• Jesus is permanently in the form of God. From birth he is holy and the Messiah. How else could he say, "if you've seen me, you've seen (known) the Father"? Being in the form of God was permanent and unchanging - except if he sinned.
• Jesus is the holy son of God - not only without sin, also without the corruption caused by sin and the alienation of (spiritual) death all men have suffered since Adam ate. His spiritual connection with God is unimaginable! Suffice to say, having this status of being one with God (not a concocted one-substance) grants him the favour of asking for anything he desires - legions of angels for example or myriad other things.
• This status is not remotely useful in accomplishing his mission to, and completing, the cross. He could not sin even though fiercely tempted or he would not be the 'unblemished Lamb' anymore and could not save himself let alone all creation.

In the days of his humanity, he offered up both prayers and pleas with loud crying and tears to the One able to save him from death, and he was heard because of his devout behaviour. Heb 5:7

• Knowing that Jesus could "do nothing of himself" aligns with his total dependency on God for all his needs to avoid sin - to avoid putting his will before God's. It is this total dependency that Jesus speaks of when he says he 'emptied himself'. While he was the form of God, he chose the attitude, the humility, the obedience of a servant. This had to be a voluntary choice made in love, trust and faith in his God and Father's plan of salvation - which he was the only key - the cornerstone planned from eons earlier. There is no place in this titanic struggle for victory over evil if he used personal power or influence as the son of God. Pride, vanity, self-indulgence, self-will, arrogance could not win this fight - they were the very things he was fighting in the devil. Jesus could use only the tools of utter dependency on God and His spiritual provisions.
• He was born like us. The gospels tell us nothing was unusual about this baby boy except he was without sin, holy, and miraculously from a virgin mother Mary. He said,

"but now you seek to kill me, a man who has told you the truth that I heard from God." John 8:40.

• If we make him more than a man (and nowhere are we clearly told otherwise), don't we make him a liar? The very test of God's truthful spirit is that Jesus came in the flesh - like us. Not as a God/man hybrid with two-natures! 1 John 4:2

it seemed good also to me, having been acquainted with all things carefully from the first, to write with method to you, most excellent Theophilus, 4so that you may know the certainty concerning the things which you were instructed. Luke 1:3-4

• Nothing in any Gospel or Epistle speaks about a pre-existing son of God, or a God becoming man, or Mary birthing God, or any other far-fetched idea about this baby born in Bethlehem. To consider or somehow insist Jesus pre-existed based on a few proof-texts is without merit, requiring a reading-in of this idea.
• When we are told Jesus is, "taking the form of a servant", no time frame is needed for this 'state'. It is a statement describing how Jesus operated, how he chose to live and function under God's direction. He was born to be a servant. Mark 10:45, Is 42:1, John 6:38, Luke 22:27.
• all the time being a servant, he is still in the form of God! Paul, the same author says, Col 1:15 He is the image of the invisible God. Image, form, representation...

He is the radiance of His glory and the exact representation of His nature Heb 1:3 NASB

• All these terms Paul employs help to put the 'form of God' in the proper perspective. Of course these states are relevant when Jesus walked with man on earth. He set the example of how to live under the one true God - being the form, image etc. while in the flesh - all the way to the cross.

• No time frame required for being one or the other. While Jesus had great power at his disposal, he was required to live as we do, being made like we are, tempted as we are;

he had to be made like his brothers in every respect Heb 2:17

• Either he was - as a man like us, or he wasn't! Being a God/man is not like us - to think so is irrational! And so we have another verse that is ignored in favour of another narrative - instead of the plain and simply understood message about the Christ, born of a woman, died as a man, just as we do, who waited in the dirt for his God to raise him and then rightly exalted and honoured him above all, making him heir to His things, judge and life-giver. Heb 1.

• As the holy man who had God as his Father, Jesus had a certain equality in the sense of having heavenly resources and status. They were his by birthright, but he didn't aspire to glorify himself in this grand state, he didn't seek to raise himself to be with God before his time and swan around in heaven abusing his privilege. No, he had a mission to accomplish and his heart was set on that - the glory would come later - not by taking it (making himself equal) but by being rewarded by his God at the proper time.

• Jesus 'emptying himself' also aligns with;

Although he was a son, he learned obedience through what he suffered. Heb 5:8

• Even as the son of God(!) he had to live out his whole life as a humble servant of God's purposes. This was a process - a continual emptying until his final breath. Always putting God's will first and not his own - even though, as we are told, he dearly wanted to - 'take this cup from me, but not my will...', and many other occasions.

Conclusion

The concept of kenosis as touted by OP is based on several unscriptural ideas - an incarnation, Jesus being part of a trinity, Jesus, therefore, being God, thus also requiring Jesus to have two natures - a hypostatic union! And so the confusion with Phil 2 is understandable when read with all that theological theory in mind.

Jesus was in the form of God and the form of a servant concurrently. The form of God he had from birth, being holy, w/o sin etc. and never lost his form and image of God. The form of a servant increased gradually through his persistent obedience to God (in the face of increasing temptation) until the cross - by putting God's will before his own. There is no time frame for somehow emptying himself of Godliness and becoming as a man - an absurd idea to begin with. God IS God, no amount of sophisticated and mysterious words can justify God becoming a man - made like us in every respect.

Caveat: this is a difficult sentence in general and there is no settled translation.

However it's translated, it's easy to make a subtle assumption about the text that isn't actually there (although a straightforward inference coming from a trinitarian position).

In the article Philippians 2:6-8 the authors conclude

"The verse is not speaking either of Christ’s giving up his “Godhood” at his incarnation or of his God-nature being willing to “hide” so that his man-nature can show itself clearly. Rather, it is saying something else. Scripture says Christ was the “image of God” (2 Cor. 4:4), and Jesus himself testified that if one had seen him, he had seen the Father. Saying that Christ was in the “form” (outward appearance) of God is simply stating that truth in another way. Unlike Adam, who grasped at being like God (Gen. 3:5), Christ, the Last Adam, “emptied himself” of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men. He humbled himself to the Word and will of God. He lived by “It is written” and the commands of his Father. He did not “toot his own horn,” but instead called himself “the son of man,” which, in the Aramaic language he spoke, meant “a man.” He trusted God and became obedient, even to a horrible and shameful death on a cross."

So it's not that there was time 1 'he empties himself' time 2 'he is born'.

To answer the questions

1. He emptied himself of all his reputation and the things due him as the true child of the King. He lived in the same fashion as other men.

2. "How can one empty oneself by birth[?]" The text doesn't quite say this, and Young's literal translation reads "but did empty himself, the form of a servant having taken, in the likeness of men having been made". So the Biblical Unitarians in the article quoted above would say it's a misreading of the text. The emptying doesn't happen before, or really even starting with his birth, but at some point in his life (presumably with a gradual increasing awareness as he grew up that he was the Messiah), most notably dying on the cross.