Is there any way I can teach Signal Beam to Espeon in Pokémon Y? Or does it have to learn through the tutor in Gen 5?
Espeon cannot learn Signal Beam in Pokémon X and Y.
So the only way to get an Espeon with the Move Signal Beam in your Pokémon X and Y Game would be to transfer one over from Black and White 2 using Pokémon Bank.
Espeon's Signal Beam is lasted as a transfer only move as per