I originally designed FlatBuffers for games (though admittedly more for things like level data or save game data than network packets), so I'd think it is pretty suitable. I had actually used Protobuf on a game project just before, and its performance problems led directly to the no-unpacking no-allocation design that FlatBuffers has.
So FlatBuffers will make an incoming packet waaay faster to work with than Protobuf. On the downside, Protobuf tends to be a little smaller, so if bandwidth is a greater concern than (de-)serialization speed, you might still prefer it. Additionally, receiving data over the network raises the question of how you handle packets that have been corrupted (or intentionally malformatted by an attacker), and in the case of FlatBuffers you'd need to at least run the "verifier" over the packet before accessing it if you don't want your game servers to crash when this happens. That slows it down a little bit, but is still fast, i.e. still doesn't allocate etc.
Cap'n Proto will perform similarly, though does have the downside that all fields take space on the wire, regardless of whether they're set or not. So which is better depends on the kind of data you want to send and how it is likely to evolve.
Frankly, for the absolute highest performance (and lowest bandwidth) game networking you still need a custom encoding.