Three things.
First of all, a clarification. This was meant for a retaliation for the American burning of York's legislative house. That's all, and that's why only government buildings were burned. It's conceivable that some British commander might want to punish America further, or perhaps some undisciplined British soldiers take it upon themselves to light a few extra fires. Unlikely, but plausible.
Second, it was a HUGE violation of war principles to burn down civilian buildings. This is going to be a big hit to British/American relations. In the long term, they'll get over it, but it might have a bit of an effect in the years after.
Third, to answer your question about what'll happen to the capital... they'll rebuild. Maybe a temporary capital in Philadelphia for a couple of years, but that's all. Remember, in 1814, Washington was still a young city. Construction only started in the 1790s. It's not like there was a modern city with huge infrastructure that would take decades to repair and rebuild... especially since it's not like the Brits will completely erase every building and piece of infrastructure.