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A patch of a flag is not aA patch of a flag is not a flag. The situation that brings this question out is that a flag in itself cannot be used as clothing. That means that you cannot take a flag, cut it up, make a shirt and wear it. It does not prohibit wearing a flag patch on a uniform.

2015 Special Edition Garden GuideCooking Fresh with The Old Farmer's AlmanacThe Almanac Monthly Digital MagazineWhat the heck is a Garden Hod?