I am not sure. I know that they will not fit into the USPS Priority Mail Rectangular Medium Flat Rate Size Box for $11.35--which is the one I have currently. (I checked this morning to see.) I don't know which USPS Flat Rate Box Size you are talking about unless you are speaking about the Large One--which I do not have. I would have to get that one from USPS to see if it would work. Possibly it would work! Thanks for the interest in the items. Sincerely, Leona Sellers