Yes, trade boost, Amie boost and Lucky Egg boosts all stack with each other. Trade boost is 1.5x (Would be 1.7x if it's from a foreign country but I'll assume it's not), Amie affection boost is 1.2x, Lucky Egg is 1.5x so the total EXP multiplier would be 2.7x (3.06x if it's a Foreign Pokemon) the normal EXP.
Multiply this by another 1.2x if the Pokemon is above the level it evolves, but hasn't yet (this is new to Gen 6, like Amie's affection), but this won't apply to Scyther since it doesn't have an evolution level. You can then boost it even MORE using the EXP O-Power, the multiplier depending on the O-Power level.
This page has information about the formula and what each part relates to:
And here's an image of the base formula, I'll quote the relevant parts you're asking about:
e is equal to... 1.5 if the winning Pokémon is holding a Lucky Egg
f is equal to... 1.2 if the Pokémon has an Affection of two hearts or more
t is equal to... 1 if the winning Pokémon's current owner is its Original Trainer
1.5 if the Pokémon was gained in a domestic trade
Generation IV+ only: 1.7 if the Pokémon was gained in an international trade