Well, after going through 517 last names of "Dow" and company "D" and their regiment was at Gettysburg broke down like this.

1) Thomas A. Dow, 20th Massachusetts, "C" and "D" companies
2) William Down, 5th Ohio, "B" and "D" companies
3) Reuben B. Dow, 19th Mass also listed in 20th Mass, "D" Company
4) William E. Dow, 74th NY, "D" company

The 5th Ohio is a possible at Culp's Hill (Pardee Field)
The 19th Mass and 20th Mass were in the thick of it during Pickett's Charge.
The 74th NY, fought in the 3rd Corps and went face to face with the 17th MS ( Doubtful the 17th MS lost a flag)

I believe it is between the 19/20th Massachusetts at Pickett's Charge, but I will not rule out the 5th Ohio at Pardee Field.

Certainly "Dow" captured a flag that is unknown and might one of the "Unidentified" captured flags.

Cheers,

Shawn Prouty