im currently playing through the legion quests and was wondering if any of the companions can use the legion armour?

No, at least I doubt it.

Legion is a faction armour, only NPC's that belong to that faction can wear said armour.

Maybe there is a mod already, or you can use the GECK to copy paste a non faction version..
I mention this due to the picture you have, being from a modded game.

No, Legion armor is indeed faction armor, and since there is no Legion follower at this point, you can not get them to wear it.

I think you may be able to give them Legion headwear though. At least the Recruit Helmet does not count as faction armor, maybe you can even get them to wear a Legion Centurion Helmet.

Edit: By the way, some companions (Arcade, Boone, and I think Cass as well) despise the Legion and at least Arcade and Boone will leave if you're on good terms with them. Lily and Raul won't care though, Lily doesn't care about the Mojave's factions, and Raul actually believes there are good points about the Legion. Still won't wear the armor though.