What is the scriptural basis for the Holy Spirit speaking to you through other people's words?

This view is actually based on overall understanding or the revelation of the scripture; that God reveals his truths and communication through various means. We know of examples where God even opened the mouth of a donkey and made him talk. (Numbers 22). In the New Testament Jesus clearly promised us of the works of the Holy Spirit (John 16). Thus it is rather an implicit case from the whole Bible that we learn that God or his Spirit might talk or communicate with us indirectly, rather than a heavenly voice or direct communication.

Romans 1:20 For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. (ESV)

(James 5:19-20) 19 My brothers, if anyone among you wanders from the truth and someone brings him back, 20 let him know that whoever brings back a sinner from his wandering will save his soul from death and will cover a multitude of sins. (ESV)

2Tim 2:21 Therefore, if anyone cleanses himself from what is dishonorable, he will be a vessel for honorable use, set apart as holy, useful to the master of the house, ready for every good work. (ESV)

1Cor 3:9 For we are God's fellow workers. You are God's field, God's building.(ESV)

1Thess 5:11 Therefore encourage one another and build one another up, just as you are doing. (ESV)

If his attributes are revealed to us through nature, his voice is also revealed to us through subtle indirect things, not just through people's advice but through anything. It depends on the us as to listen to him.

General reference on God's guidance that you might use as reference:

Gen 12:1; Exod 13:21; Exod 15:13; Exod 33:13-15; Num 10:33; Deut 32:10; Deut 32:12; 2Sam 22:29; 2Chr 32:22; Neh 9:19-20; Ps 5:8; Ps 23:2-3; Ps 25:5; Ps 25:9; Ps 27:11; Ps 31:3; Ps 32:8; Ps 48:14; Ps 61:2; Ps 73:24; Ps 78:52; Ps 80:1; Ps 107:7; Ps 139:9-10; Ps 139:24; Prov 8:20; Isa 40:11; Isa 42:16; Isa 48:17; Isa 55:4; Isa 57:18; Isa 58:11; Jer 3:4; Luke 1:79; John 10:3-4; John 16:13

This question reminds me of the interview of Andrew Klavan on Jewish Voice on his book The Great Good Thing: A Secular Jew Comes to Faith in Christ where he explained how God kept calling and helping him through subtle messages and things in life. He shared an incident where as an unbeliever he was on the verge of committing suicide, but he saw a Christian baseball player on TV whose direct pro-christian messages were so annoying to him; but that night the player said "sometimes you have to run in pain", an indirect secular message which saved Andrew from committing suicide. He of course later realized that God was helping him all along.

God did in times past use prophets, dreams, and yes even a donkey to reveal his will to man. But in these last days he has spoken unto us through his Son Jesus (Heb. 1:1) Jesus has revealed the mind of God to us through the Holy Spirit, for the Spirit will not speak of himself but whatsoever he hears that's what he speaks (John 16:13-14). How then does the mention of something quitting (like the wind) seem like a word from the Lord? I believe the answer is found by looking at two passages. Jeremiah 31:33 and 2 Cor. 3:3 both tell us that the Holy Spirit writes the word in our heart. Because the will of God is in our heart our conscience will either condemn us or not (1 John 3:19-21). That is God's way of moving us to repent, the goal is to have a conscience free of guilt. My prayer is that you will yield your will to the will of God.

I do not think that there is any direct scriptural basis for God speaking through other people. This means that (to my knowledge) there is not a specific Bible verse that iterates this crystal clear.

But after close inspection, you can see that God speaks in miraculous ways. He used Balaam to speak. Even though Balaam was not a Christian, and was rebellious, God used miraculous ways to speak.

Know I know this isn't exactly the kind of situation you're talking about, but it is something to think about. God will talk to you in many different ways.

Sometimes while I'm coding, I'll listen to (christian) music as well. Twice in the course of a half-hour, the words I was typing matched with the song. And it just got me thinking, "Wow, God is amazing. He can use any method to speak." He can use any method he wants to talk to you. Dreams, other people, even sitting down in your room! Yeah, that happened. God uses amazing ways to accomplish his will. And if speaking to you is His will, it'll get done.