There is a default limit of 200 players in a game session (doc), and there is a hard limit of 50 concurrent processes (1 process = 1 game session) in a fleet instance (doc). There is a default limit of 20 instances per fleet. However, number of instances per fleet is much easier to approve, so in theory you could have infinite number of instances per fleet, and therefore infinite number of game sessions per fleet.
However, realistically, depends on your player traffic, you may not be granted that many instances in a fleet.
Also, 50 is the cap of concurrent processes. Depends on the computing power of your instance type and how intensive and optimized your server is, you may not even reach the cap of 50.
One good way to stress test is, start with 1 fleet, 1 instance and 1 to 5 concurrent processes, create game sessions on them, connect players to them, and then monitor the CPU/network IO/Memory usage on the instance (via SSHing to the fleet and run
top, or use GameLift AWS console), then add more processes or players until you reached desired amount of saturation.