Despite the precise design we've reproduced dates back from 1669, the use od red flags with a cross flanked by either the pontificial keys or images of St. Peter and St. Paul is attested from times of the Second Crusade. Red flags were still in use by late XVIII century, but the change to a red and yellow flag seems to be attested already in the previous century.
Sources: Anonymous manuscript from 1670, reprinted in Amsterdam 1966 as «Flags of the World 1669-1670» | Flags of The World (FOTW) website:Vatican - Historical Flags
Sizes: ensign W12 x L18 mm, mast flags W8 x L12 mm, jack W6 x L9 mm, pennant W4 x L48 mm.