Flying Tigers never faced the A6M2. They fought the Ki-43, which was armed in the first version with two 7.7mm machine guns. Later versions increased the size of the guns, but it was still only armed with two 12.7mm machine guns.
Many pilots just called any Japanese fighter a "Zero", but that is definately not true.
Nakajima, the company that built the Ki-43, didn't even submit a design for the Imperial Japanese Navy due to the requirements of speed, range and armament, only Mitsubishi did. Nakajima considered the requirements contradictory. Mitsubishi pulled it off, but had to sacrafice any semblence of protection to do so.