Can I brine meat after cooking it?
It won't do anything useful.

Brining works on raw meat by denaturing some of the proteins inside the cells so they gel and hold tightly onto their water. It also gets tasty salt in.

Cooked meat has already had its proteins denatured by heat. Brining will not cause the meat to hold on to any new water. 

Basically all it will do is wash away some of the surface flavor into the brine.