I want to make a competitive team based around Mimikyu and Sylveon~
I wanted to include Alolan vulpix but it isn't very good unless I evolve it so i dropped it.
I might bring Charizard Y on the team since Arcanine is 4x weak to water.
I would advise against using both Mimikyu and Sylveon on the same team. Although Mimikyu is primarily a physical and Sylveon is special, they share the same weaknesses and can both struggle with some of the same Pokemon. Maybe if it was a mono fairy, but it's clearly not because you're considering Charizard Y?
It would help a lot to know what competitive meta you are building for. Is this for a smogon tier or for VGC?
If we're going to assume this is for OU on Smogon, here's some options.
Mimikyu @ Life Orb/Ghostium-Z
EVs: 252 Atk / 4 SpD / 252 sp
- Swords Dance
- Shadow Sneak
- Play Rough
- Shadow Claw
Mimikyu Team Mates
Mimikyu benefits from having Sticky Web set up to slow down Pokemon that might be faster than it, so Smeargle, Galvantula, Araquanid or Shuckle could all be paired with it. Frankly though, none of them are any good in OU so I wouldn't recommend this tactic for someone new to competitive. You'd be better off spreading paralysis and making good use of priority.
You're going to want to check Steel types and set hazards, so Heatran or Ferrothorn would be great choices for teammates. Heatran totally walls most Fire and Steel types, has some offensive power and can also set up hazards to whittle down the enemy team for Mimikyu to clean up. Ferrothorn can also check most Steel types, maybe a few more than Heatran even since it's Ground neutral and can set hazards and spread paralysis. It doesn't have the same offensive presence though. Magnezone is also an option for dealing with Steel types since it's a powerful Special Attacker that can trap them with Magnet Pull - it also can't be touched by Toxapex which Mimikyu has trouble with (same for Ferrothorn).
Wallbreakers are a good idea too. Mega Charizard Y, Ash Greninja, Magearna - Pokemon that hit very hard and can remove the bulkier or problematic Pokemon so Mimikyu can clean up in the late game. Good users of U-Turn or Volt Switch like Landorus-T (best mon in OU), Assault Vest Magearna and Greninja also pair up well with Mimikyu since they can get it in without breaking its Disguise.
I haven't done a Sylveon set or given you team options for Sylveon, because honestly Mimikyu is a much better choice if you ask me. But if you decide you'd prefer to use Sylveon, let me know and I'll see what I can do. I definitely would advise against trying to use both though.