Obviously the inanimate object in question should also be owned by the person who is doing the burning.
Everybody equates the amendment's use of the word "desecration" with burning. If and when this abomination ever passes, it will then be up to Congress, the Courts, every local cop, to figure out what desecration means. See a young lady with a handbag, or jeans with a flag incorporated into them? Find it offensive (I personally don't like that kind of flag use). Call 911 and press option 2 "if this is an emergency where something or someone really offends you."