I already have a default slot in my AnimGraph. For my Flying Logic, should I make another one ?
That seems like the main out pose so there shouldn’t be a problem there.
You should be able to trigger montages using either of these:
If you’re using the Play Montage node, make sure to plug in your mesh into the Skeletal Mesh Component pin.
Also make sure to trigger the montages only once and not repeatedly, and you should be all good 
So I pulled out from get actor of class ( actorclass:CharacterA ) > Return value > Get mesh
and that looks like this Image Below:
I do not have any other Mesh Variable available to use, cause this is Player Controller
You can just drag the mesh component from the Components window (which should be located on the top left by default)
If you’re not handling this in the character blueprint but rather the level blueprint where you handle the character switching mechanism, please share the full code. Maybe you’re trying to access the mesh after the character is destroyed.