What did the British offer to enslaved African Americans in exchange for looting and burning the Capitol Building in Washington D.C.?
The question seems to indicate that Black Slaves burnt the Capital Building in 1814. I would have to see real evidence of that because I'm unaware of it.
The peace deal at the end of the War of 1812 was "status quo ante" or like it was before. The peace turned back the gains and losses to the territorial map before 1812. Basically the war was a draw and the peace reflected that.
The British did pay for the loss of slaves from slave holders. The slaves left with the British forces and because slavery was illegal in Britain, were freed. The Slave owners claimed capital losses of the costs of the slaves as part of the peace deal. Britain paid the costs.
Undoubtedly British soldiers burned the Capitol Building in 1814 but whether Blacks assisted in any organized fashion I have no proof of. Rather more likely is that when their owners fled they followed the British Army North to Canada and freedom.