team recommendation?

If you are a NA player, there is no "good quick team" before Skadi's coming 2 year later.

If you want to build a team around Kuro, art team is always the best, no need to have Jack in team.

If you want to build a team around Jack...There are two general ways:
First Jack as major DPS and hitter, then use 2030 dual supports no matter Waver or Hans. However they are also vulnerable if you are fighting with riders, so caster support is not recommended in some cases, then using demi-support (with more art/quick card than buster card) with dual Jack is a better choice.
If you want to make Jack' NP Nuke versus females, use OG Shishou, Atalante as support. But there is no consistency if you picked them, only for Jack's amazing NP.
Just remember quick chain (no 2030) or AQQ (if you have 2030) is key for Jack build-ed team, normally the less burst card the better.

The another way is to use Jack as star generator and 2nd hitter. It is better to team with riders like Drake, Kintoki and Ushi, or other servants with decent star adsorption (Raikou, Lancer artoria alter, Okita, Shishou OG, etc) skill. However Jack's 3 quick card could be either a burden or advantage for these 1st hitters.
Kuro is not recommended since she has either no star adsorption skill, or no buff for Jack and team.
But I dont think it is a "quick team" in this case,

I'd recommend using Billy as apposed to Chloe for a quick team but if you're set on Chloe she's fine. Hans is amazing on quick teams because the passive star generation from innocent monster and his party wide crit damage buff are extremely useful and help with turns where your cards might not offer much star generation.

Waver obviously functions well with his ability to charge an ally's NP by 50% and his attack + crit buffs can lead to massive damage. If you don't have him there should be no shortage of him in your supports. His star gen is really bad though so it would probably be better to save him for boss fights or maybe gaining crit stars then substituting out someone for Waver's buffs allowing nukes.

I'd recommend you check this out too. https://grandorder.gamepress.gg/staple-quick-team

What they've said. Billy would be the quick dps/Archer. You could also consider OG Shishou with her quick np and quick up as well as kintoki rider. The reason quick teams are not meta in NA is purely due to their lack of support. Skadi will fix this in 2 years.

For Chloe specifically, an arts crit team would be best which would involve herself and whichever combo of jack, Tamamo, and waver you feel like using.