Here are some ways that you can get your teams kit into Zwift, so you and your teammates can represent your time while riding through the world of Zwift. There are a few ways to do this, and none of them are very easy.

Have a team in the Premier Division
In order to get a custom kit, you team must win the A category Zwift Racing League D1, then beat all of the other D1 teams before making it into the premier league. Part of making it into the premier division includes getting your own custom kit. Once you make it in, you just need to send your design into Zwift, and they will get it into the game. Typically kits are added in the monthly game releases, so it might take up to a month for your kit to actually show up in the game. Zwift then needs to add the kit to your account in order for you to wear it.
Have LOTS of members
At first, only the biggest of the biggest teams had their kits in game, but now Zwift is adding in game kits to smaller teams of around 200+ riders. You are more likely to get your kit in game if you lead weekly group rides, and have a good reputation.
Event series/race series that requires a kit
Lots of racing series and event series include an in game kit, which can be unlocked or used by the users. This is a good way for companies that also have a Zwift team to get their kits in game for their riders to use.
Mark Cote, a member of the Zwift Staff posted this on the forums around 10 months back. These are the factors considered when adding a kit to the game.
“-Zwift or partnership campaigns requiring new kits
-Racing leagues (often with broadcast components) that require differentiated brands to know who’s competing versus each other (Super League Triathlon, Zwift Racing League Premier Division, etc)
-UCI ProTour Team requirements, as well as national federation requirements for sanctioned eSports competitions
-Prominent Event Promoters who benefit the community by representing their identity on kit
-Strategic partners who require brand presence in the Zwift ecosystem“
Note that this is a manual process, and Zwift says that they have to design the kits pixel by pixel, which is very time consuming. Getting your kit in game has gotten a LOT easier in the past few years. At first, Zwift would just add a few kits each month, now dozens of teams are getting their in game kit each month.