In modern U.S. colloquial English, "Thanks for your help" is correct. There's nothing wrong with being simple and direct. The important thing is to thank the person. The exact words you use don't matter. "Thanks for your kindly help" sounds odd to my ear, courtly or old-fashioned. I can't think of any natural-sounding way to add the word "kindly" or "kind" to that phrase. If I wanted to intensify it, I would say "Thank you very much for your help," or I would strengthen it by adding details--"Thank you for the extra time you spent helping me" or something like that.

'Thanks for your help' is correct although a little short. If you wanted to be nicer then 'Thank you for your help' is better

These are all simple correct examples: Thanks for your help. Thanks for your kind help. Thank you for kindly helping me. Thank you for being so kind and helping me. Thank you for helping me so kindly