Actually, there is no strong link between the burning of Canadian towns and the burning of Washington. I was surprised to find that out when I was writing an article on the subject, see:
"Why the White House was Burned: An Investigation into the British Destruction of Public Buildings at Washington in August 1814,"
JOURNAL OF MILITARY HISTORY, vol. 76, no. 4 (October 2012), 1095-1127.
It should be noted that the public buildings at Washington were perfectly legitimate targets of war as much as there were rules for civilized warfare in 1814, a subject I delve into in the article. Also, the Britsh army maintained excellent discipline while in possession of the American capital and did not loot or plunder civilian dwellings or persons. Only one non-government structure was burned and that was a house from which a sniper fired at General Ross, the British commander..
This is in distinct contrast to the behaviour of French armies of the period.