Since your tailpipe has a heat shield I think it is safe to assume you have a 2010 Grubee Skyhawk kit.
I just got my first 2010 in myself.
Also...although I don't like the idea...some have removed the rag joint on the outside leaving sprocket to spoke contact.
I don't much
like leaving the outer rag out either, but sometimes it does seem to be the best option.
Case in point the Pacific Capeland I am just wrapping up today.
Using the outer rag the sprocket hole would not reach the hub, and it was too wide.
When you can't use the hub to help center and sprocket and keep it centered you are relying on the rags and spokes to keep the sprocket centered and that stinks in my book and could very well be the cause of your chain problems.
The sprockets on the Grubee kits has a shiny side and dull side, the shiny side usually goes out.
Just leave the outer rag out and flip the sprocket so the shiny side is in up against the spoke nubs.
Once you get all the bolts in and loose fit, turn the sprocket in the direction of drive (counter clockwise from the outside) until the bolts come up against spokes and tighten it down in a Star pattern, just a couple of turns on each as you go like when tightening lug nuts on a car wheel to insure a good true even fit.
This will prevent the sprocket from rotating on the spoke nubs, as it would until gets there anyway.
This leaves the dull side out, which works out dandy as it is easy to paint to match the bike.
Note that sprocket fits perfectly over the hub, the dust cover goes on without a problem, and the coaster brake has no issues either.
Finally, take the extra step to size the drive chain so you don't need a tensioner on the drive side!
The kit chain has a master link, take it out and thread the chain through the motor sprocket so the bottom side reaches to the back of the wheel sprocket with the pedal chain on but with some slack (unless they just happen to match perfect of course).
If the drive chains don't match ends (two thin ends for the master), pop off the fat one and drop in a 1/2 link.
Once the wheel is on and tight with no drive side tensioner, put the tensioner on the seldom used pedal side to take up it's slack.
You can use the big bulky kit one (and paint it too if you want) or you can get a much small one from a bike store too.
You can get a chain breaker from a bike store or Ace Hardware for about $10 and a 1/2 link is like $1 if you need one.
I hope that helps you. All I know is it works for me.