Here is a link to the flag of the United States Coast Guard, which does not look anything like your description.
But here is a link to the ensign of the United States Coast Guard, flown by its ships:
No, it did not.
Under Spain, viceroyalties had their own flags, and in this case the flag of New Spain was the relevant one. After independence, Mexican state flags and coats of arms were slow in developing. To compare to two more populous provinces, Jalisco only created its flag in 1972, and Durango still does not have one (it does have arms).
I don't know what it is. But I can tell you what it isn't.
This doesn't appear to be any US city, state, governor, nor county flag.
However, those lists are not exhaustive. Check the flags of local government.
It's not likely a historical Confederate States of America (CSA) flag, CSA flags usually, but not always, have three stripes. It could be a modern ...