Thanks for your thoughtful questions. The U.S. Flag Code, section 4-(d) states: "The flag should never be used as wearing apparel, bedding, or drapery...." While it's not misquided to feel its wearing as a mark of patriotism, others may feel differently--just as you do about Madonna's use of it. As far as disposal of the shirt, since technically it isn't an American flag there would be no harm in disposing of it however you wish, which could include the option of a proper burning and burial ceremony.
If you want to display the flag on a personal level, there are options available for patches and pins which are appropriate, respectful and patriotic.