Did you orient the ring gaps? And did you separate the oil control gaps? Sounds like you are sucking crank case oil up into the chamber. If it keeps it up and never goes more to blue as if the rings are seating, you may need to go back in.
How much gap did the rings have? And, that Briggs has an iron liner, right?
Disconnect the crankcase breather where it goes into the carburetor. If it is pushing oil out of there, you have a compression problem. If not, and it still smokes, you could have- a broken ring, or scraper ring installed upside down.