That "blanket or flag" is folded in half and is the seal from the state of Arkansas. I have seen other people point out that the furniture in the picture perfectly matches images from Camp David when Bush was in office. Clinton was Governor of Arkansas before being POTUS so this was very likely taken while Clinton was President. Either Trump visited Clinton at Camp David and it is someone he knew but clearly mistook, or he was going through pictures during his recent visit to Camp David and his dementia is progressed enough he thought this was one of his daughters.