The phrase is more commonly "kind support," so the sentence would be:
Thank you for your kind support.
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"Kindly," as you know, can be used as an adjective, even though it has an "-ly" ending. The suffix "-ly" adds the idea of "like" to the noun or adjective it attaches to.
The words "kind" and "kindly" are similar, and sometimes interchangeable. Here are definitions from the American Heritage Dictionary*:
"¢ kind
adj., kind"¢er, kind"¢est.
1. Of a friendly, generous, or warm-hearted nature.
2. Showing sympathy or understanding; charitable: a kind word.
3. Humane; considerate: kind to animals.
4. Forbearing; tolerant: Our neighbor was very kind about the window we broke.
5. Generous; liberal: kind words of praise.
6. Agreeable; beneficial: a dry climate kind to asthmatics...
...SYNONYMS kind, kindly, kindhearted, benign, benevolent. These adjectives mean having or showing a tender, considerate, and helping nature. Kind and kindly are the least specific: thanked her for her kind letter; a kindly gentleman
"¢ kind"¢ly
adj., -li"¢er, -li"¢est.
1. Of a sympathetic, helpful, or benevolent nature: a kindly interest; a gentle, kindly soul. See synonyms at kind1.
2. Agreeable; pleasant: a kindly breeze. ...
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Google gives 1820 examples of "Thank you for your kind support," in sentences like this:
"¢ I've visited your site for the first time today - Great site! (Leif K. Denmark 01/99)I would like to thank you for your kind support in the promotion you have ...
Google gives 28 examples of "Thank you for your kindly support" in sentences like this:
"¢ ... Thank you for your kindly support, we are looking forward for your further support in coming activities,
Rachel
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*The American Heritage Dictionary of the English Language, Fourth Edition. Houghton Mifflin Company.