I suspect that this was not the flag of the 50th Ohio. Major Thoburn has used a somewhat convoluted sentence structure that is easy to misinterpet. I think what he is saying is that he did not want to take the risk of carrying an unknown regiment's flag through enemy lines, as simple as it would be to pick it up. He then expresses some guilt at leaving one of "our flag[s]" by which I believe he means simply a general Union flag instead of his own regiment's flag.

Ryan Toews