Flying Within the U.S. on a Foreign Passport

I live in Canada, but am not a citizen. I've lived there 60 years, but haven't got a Canadian passport, or permanent residence card yet.
I travel to the US a few times a year by car. I have a British passport which allows this, but not for me to fly into the US. I need to know if I'm already in the US, am I allowed to fly within the US? I want to go specifically from Buffalo to Florida. Any help would be greatly appreciated. Thanks

I suggest you ask that question of the airline's customer service and the TSA.

As long as you're not on any "watch lists" domestic flights don't really care about your passport status. You need to provide a valid passport that matches your ticket to get through security but that's it.

Thanks..everything I've read suggests I can use my gov't issued foreign passport and driver's license...I'll check airline too...