Looking on the internet deeply has found these results:

thanks for your kind support is the most popular phrase on the web.

thanks for your kindly support 153,500 results on the web	thanks for your kind support 1133,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Mr Crowley, many thanks for your kind words. Thanks for your kind words of support. I wanted to thank you for your kind recommendation. Thank you for your kind words, chancellor. I'll do my best... as for your kind support. Mr President, thank you for your kind words of support which I trust apply to every proposal in the report. Thank you one and all for your kind applause and your generous support. Thank you for your kind blessings.

thanks for your kindly support

153,500 results on the web

thanks for your kind support

1133,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Mr Crowley, many thanks for your kind words.
Thanks for your kind words of support.
I wanted to thank you for your kind recommendation.
Thank you for your kind words, chancellor.
I'll do my best... as for your kind support.
Mr President, thank you for your kind words of support which I trust apply to every proposal in the report.
Thank you one and all for your kind applause and your generous support.
Thank you for your kind blessings.