I did some googling and it seems most historians view the origin of the Grand Union Flag as a mystery. I found one article by a historian who did some digging in East India company records, but he only came up with circumstantial arguments. The best argument for is the remarkable resemblance of the two flags. But there are several arguments against. The Admiralty disfavored use of the Company flag outside territorial waters and directed Company ships sailing to England to use the Red Ensign. There was also no direct trade between the Company and America. On the other hand, it could be assumed that Franklin and others spending time in England likely saw the flag.
On the other hand, check this out:
This is the Red Ensign, the flag of British merchantmen, which would have been seen in every port in America:
It would not have taken a lot of imagination to think of running white stripes through the red field to create 13 stripes representing 13 colonies.