I really strongly think that Lin Manuel Miranda had a Christian mindset while writing Hamilton. I think that Burr represents the devil, someone who can't refrain from sin, dragging the others down with him...
First of all, Burr is the first person in America that meets Hamilton and he immediately wants him to stop chasing his dreams. This is an anti-Catholic notion that is trying to prevent Hamilton from reaching salvation by giving charity and by improving the world, thus not allowing him to find the church to forgive his original sin.
Also, Burr embodies what God says should be avoided. 2 Timothy 3:1-5 says:
"For people will be lovers of self, lovers of money, proud, arrogant, abusive, disobedient to their parents, ungrateful, unholy, heartless, unappeasable, slanderous, without self-control, brutal, not loving good, treacherous, reckless, swollen with conceit, lovers of pleasure rather than lovers of God, having the appearance of godliness, but denying its power."
Burr loves himself more than others, saying that he is the one thing he can control and not seeking to improve the lives of any others. He never donates to charity in the musical, but he is rich, hence loving of money. As a child he ran away from his uncle which is disobedient to his parents. He is arrogant and abusive when he believes he will win the presidency and then shoots hamilton. He is ungrateful to the people who brought him to the place he is in (his father who is a preacher and his mother who is a genius). He is a lover of pleasure when he goes to Europe. Burr is clearly the anti-christ. He was also never punished for his crimes.
Burr continuously tries to suppress Hamilton's Godly nature by discouraging him, up until the point that he tempts him to sin. He tempts Hamilton by provoking him with letters threatening him to a duel, which would have Hamilton commit a mortal sin: Murder. But then, if Hamilton were to go to the duel knowing that he would remain Godly, he would have to be throwing away his life -- thus committing another mortal sin of suicide. He would not have the chance to repent from that sin and would be brought to Hell by the temptation of Aaron Burr, the devil's agent.
We do not know if Hamilton goes to heaven. Lin Manuel Miranda would rather us interpret his writings in our own way. Perhaps he prayed beforehand or he prayed on his deathbed and was forgiven by God. It is my opinion that he went to heaven because he prayed on his deathbed. Also, because Elizabeth sees him at the very end of the musical. But maybe she went to Hell too, that is a post for another time.
I hope you enjoyed my Hamilton analysis.