I saw a flareon once! I lol'd, clicked earthquake on my life orb garchomp, and it died with its jolteon buddy. In all of my playing, I have seen maybe two flareon not on a dedicated eeveelution team, and none did anything before dying.
Jolteon, as sarsya said, is good as a glass cannon, but
252+ Atk Life Orb Talonflame Brave Bird vs. 0 HP / 4 Def Jolteon: 153-181 (56.45 - 66.78%) -- guaranteed 2HKO
I wouldn't call it one of the best just because it can live a brave bird. This is doubles so protecting with one then attacking with another is so common a sash set is basically needed. In general though, I would still say jolteon is one of the best eeveelutions for doubles, mainly because most of them suck. Same deal with espeon.
Vaporeon is stally so not really suited for doubles, but I've seen a few work out. Usually it prolonged a game for a few turns but never did much to me other than scald hax + protect spam. Some sets also run wish, but wish is mediocre in doubles. I guess you could say its just not suited for doubles. In doubles, it's VAPOOREON. Same deal with umbreon.
Its too early for me to say anything about Sylveon, I haven't seen many.
I think I have only ever run an espeon myself though, just to test sticky web bounce at the beginning of gen 6, but it was too frail and was off my team in no time.