I don't have a FireStick, but I use Harmony- not sure why the FS would be confused since there's no two-way communication between it and the equipmnent. I can understand seeing problems if a command from one remote is still being sent when a command from the other remote is being received- some equipment acts like it's blond or stunned when conflicting commands come in.
Battery life is one thing that makes a difference- I have a Harmony Companion that uses a 2032 disc battery and when that is starting to go, the hub won't always respond to the remote, so I test it by using the phone app- if it works immedately and every time, I replace the battery but sometimes, neither works and I just have to wait.