Non start - 1979 125cr - help please

Engines need fuel, compression, spark and the correct ignition timing to run. Assuming the engine ran ok prior to the rebuild then something is missing or out of range in 1 of those 4 variables. Eliminate each variable one at a time.
Fuel. The engine runs if you squirt gas in the plug hole so this would indicate the timing, compression and spark are good.
Compression, see point 1. It ran however do a compression and leak down test.
Spark. See point 1 again. It ran so spark and timing should be ok. Check your flywheel woodruff key is intact.

It sounds like a fuel/carb issue.

Here is a link to the complete ML/MK Workshop Manual.

http://www.3medesign.com/tech-data/MK-ML_workshop_manual.pdf

If you haven't fixed this already check the woodruff key hasn't snapped causing the ignition timing to go out. Happened to me.

If you are getting a backfire through the carb suggests you might have a problem with the reeds, broken or not shutting properly?