Haha, playing around with reversing flags was the first thing I thought about trying.

The surprising result (to me at least) was that out of 270 valid letter combinations, 105 can be reversed. The odd number is easy to explain: letter pairs like MM => MM can add a single flag instead of a pair of two flags, but the fact that almost two out of every five flags are reversible feels pretty high to me.

> but the fact that almost two out of every five flags are reversible feels pretty high to me.

I think some letter-frequency analysis can probably explain it. Given the fact that certain letters are less likely both as the first slot and second (e.g., there are only 4 country codes that start with J, and 3 that end with J), the letters that can be used as both first and second characters are over-represented.

It's the same as how far more English language words can be reversed to make other valid words than you would expect if the letters were equally-frequent and arbitrarily arranged.