What are the biblical arguments for and against the "two books" view of God's revelation?

Mmmmmmmm....bacon.

Sorry, got distracted. I just googled "Francis Bacon two books quote":

• "God has, in fact, written two books, not just one. Of course, we are all familiar with the first book he wrote, namely Scripture. But he has written a second book called creation."

This statement is somewhat ambiguous and he might have meant a lot of things by this, not even necessarily that we should study nature as much the scriptures, as you suggest. Was he talking about salvation, appreciation for God's creation, or how God's creation can lead someone to him, or something else?

One way that Francis could have meant it was that creation, or created things, can bring someone to the Lord. He may have been re-stating Romans 1:20 which says that no man can deny God's power because he's plainly revealed it through his creation:

Romans 1:20 ESV 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.

But regardless of how he meant it, your question wonders whether there's a scriptural basis for seeking and knowing nature and created things as much we should seek and know the scriptures: and really there's not.

Jesus seems to say the opposite of that here:

Matthew 24:35 ESV Heaven and earth will pass away, but my words will not pass away.

Going back to Romans 1, Paul says a similar thing about those that honor creation without honoring the creator.

Romans 1:25 ESV ...they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed forever! Amen.

I'm sure someone will downvote this for presenting useful information other than that which directly answers the question, but before we can really know what scripture says about Bacon's theory, we must know what he actually meant (as the other answer also points out). He clearly doesn't mean it in an atheistic sense, as if the book of creation is meant to replace the Bible or some such. We live in the age of google books, so if one wants to know what he actually meant, one can read his book here (The two books of Francis Bacon: of the proficience and ...). In there he says on page 8:

But farther, it is an assured truth, and a conclusion of experience, that a little or superficial knowledge of philosophy may incline the mind of man to atheism, but a farther proceeding therein doth bring the mind back again to religion:...

This reminds me of such passages as Romans 1 and Psalm 8 which speak of how nature declares God's existence. Context shows that by philosophy Bacon means natural philosophy, that is, what wee call "science," or simply knowledge of the natural world.

Further down, again on page 8, he says:

To conclude therefore, let no man upon a weak conceit of sobriety or an ill-applied moderation think or maintain, that a man can search too far, or be too well studied in the book of God's word, or in the book of God's works; divinity or philosophy; but rather let men endeavour an endless progress or proficience in both; only let men beware that they apply both to charity, and not to swelling; to use, and not to ostentation; and again, that they do not unwisely mingle or confound these learnings together.

That is, he does not assume that both books are to be used in the same way or treat of the same subject, as the OP apparently assumes he means. He doesn't mean that God wrote two books on religious practice. The Bible is a book on religious practice; creation is not. One is not to criss-cross (as he calls it "confound") nor "unwisely mingle" the disciplines of these two books. The phrase "to use, and not to ostentation" obviously means natural philosophy is to be studied for its practical benefits for humanity, not in an attempt to disprove the Bible.

That being his meaning, surely the Bible does not oppose it. The Bible presents itself as the rule for religious practice, but the study of nature for how to understand and use nature to our physical benefit. Certainly this is covered by

Genesis 1:28 (KJV) "And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth."

God has given man dominion over the earth, and the task of "subduing" it. Certainly with this comes the task of seeking to understand the natural world and use it to human benefit. This is the true purpose of real "science," not to tell us how the world was made or how life arose, which is answered by the Bible not "science."

I want now to also add a quote from Bacon on page 86 which demonstrates he does not intend for the book of nature to be used to alter religious beliefs:

And as concerning divine philosophy or natural theology, it is that knowledge or rudiment knowledge concerning God, which may be obtained by the contemplation of His creatures; which knowledge may be truly termed divine in respect of the object, and natural in respect of the light. The bounds of this knowledge are, that it sufficeth to convince atheism [of God's existence], but not to inform religion: and therefore there was never miracle wrought by God to convert an atheist, because the light of nature might have led him to confess a God: but miracles have been wrought to convert idolaters and the superstitious, because no light of nature extendeth to declare the will and true worship of God.

Those, therefore, who think Bacon was trying to put natural philosophy on a par with the Bible with respect to being a sourcebook of religious belief or practice, have clearly received their information on Bacon from really bad superficial summaries, and not from reading Bacon himself. For an example of such, see this article from ICR (The Two-Book Fallacy) the author of which is clearly clueless as to the authentic meaning of Bacon.