Aren’t we a bit early for the Union Jack?
Looks like its beginnings were in 1606.
Per wikipedia, that’s the flag of the Kingdom of Great Britain, used 1606-1801 and in Scotland from 1707, it consists of the flags of England (red cross of St. George on white) and Scotland ( white cross/saltire of St. Andrew on blue) one overlaid on the other. If you look closely you’ll see it lacks the narrow red saltire for Ireland( “X” type cross ) superimposed on the Cross of St. Andrew which is present on the Union Flag or Jack.
So if the ship is bound for Jamestown, founded 1607, it could be correct.