Hmm. It looks like you’ve got a sprocket that won’t work with most hubs. Almost every racing kart uses a 6-bolt-on-130-mm circle pattern. I think you’ll need a different hub, especially with a 50mm axle.
The “double D” bore of the driver is very common in the electric bike/scooter world. The website above has many options for chain types and tooth counts with that drive setup. They may even have a hub for that rear sprocket you posted above.
Hope that helps.
*Edit: They do not have a hub for a 50mm axle. I think your best bet would be to use a #35 double d driver, that way you can use standard kart gears and hubs that will fit a 50mm axle.