The answer seems too simple: other alleged divine writings are not from God because they are not among the 66 books of the Bible and, in fact, they contradict the Bible.
A Presuppositional Approach
This is a "presuppositional" approach, which means to presuppose that God exists and that His Word, the Bible, is the truth. This is the starting point or axiom.
God never tried to prove His existence or prove that His Word is superior to other writings. God simply opens the Bible with a statement of His existence and says His Word is flawless (Genesis 1:1; Proverbs 30:5). The Bible bluntly claims to be the truth (Psalm 119:160), and Christ repeated this claim (John 17:17).
In fact, if God had tried to prove that He existed or that His Word was flawless, then any evidence or proof would be greater than God and His Word. But God knows that nothing is greater than His Word, and therefore He doesn't stoop to our carnal desires for such proofs.
The Bible also teaches us to have faith that God exists and that having faith pleases Him (Hebrews 11:6). Accordingly, we are on the right track if we start with God's Word.
So how do we know that other religious writings are not from God?
God Will Not Contradict Himself
In the Bible, we read that God cannot lie (Titus 1:2; Hebrews 6:18). This is significant because it means that God's Word will never have contradictions. Though skeptics have alleged that there are contradictions in the Bible, every such claim has been refuted. This is what we would expect if God's Word were perfect.