What are the rules for flying an American flag during war?

If it is a very minor tear (less than one inch long) then it is widely accepable to continue flying the flag as long as its condition does not bring discredit upon it. Anything bigger than that you really should not fly, especially if it is a really big tear, or the end is tattered, in which case I recommend folding it up, properly storing it (in a clean, dry, non-floor/ground) place and getting a new one.