The Races are available once the ship modding tutorial is completed. This is right after you have eliminated the Fire Giant on Haven. 

To unlock racing missions, head to the Fortune's Rest outpost on the Crimson Moon.

Once landed on this planet, interact with the hologram billboard, select Crimson Moon Missions and Racing. 
 
Fly around the Fortune's Rest and look for the Outlaw Clubhouses in order to start the race!

Once a race is won, you will unlock trophies that you can deliver to Fortune's hologram. This will grant you paint jobs!
 
If you have any other questions, don't hesitate to contact us!