Google for the fabric district in downtown LA, best to go there on weekdays to avoid the crowds.
Check out Roll O Fabric in the garment district. They buy and sell surplus fabric. General info: From 110, take 9th towards garment district, they are a couple streets down from Main St on the left (not located on 9th, on a side street).
Michael Levine's, downtown, Fashion District. Either pay for parking in one of the lots of face the specter of the $80 ticket you'll get for street parking near the store. There is no safe way to park on a street in L.A. as the ticketing rules are made random and punitive to ensure a steady income of money to the black hole slush fund that passes for city government here.