Which English form is correct:
for your approval or for your kind approval ?

The phrase "for your approval" sounds more natural than "for your kind approval."

for your approval

It's correct
You might use this phrase when asking a work superior to sign off on something. More...

for your kind approval

It's not correct. Don't use this phrase.
The phrase "for your approval" is polite enough; "kind" might sound rather over-the-top.

Make sure your words are as PROFESSIONAL as you are!