"Kind of a X" and "a kind of X" are two different structures that mean two different things. It would be very strange to combine them in writing. However, in speech, someone might start to say one structure, and change to the second structure halfway through. It isn't correct, but it is a common mistake that natives would often make. "X is a kind of Y" = X IS a Y. It is one of many types of Y. A cat is a kind of animal. A novel is a kind of book. "X is kind of a Y"= X is a weak version of Y. It is halfway between being Y and not being Y. Bob is kind of a jerk=Bob acts like a jerk more often than other people do, but he doesn't always act like a jerk. We will usually use " X is kind of a Y" to weaken a statement that makes someone else look bad, or one that makes us look good. "Sam is an idiot about computers" sounds cruel. "Sam is kind of an idiot about computers" sounds more polite--it almost becomes affectionate. "I am a genius" sounds very, very boastful. "I'm kind of a genius" still sounds boastful, but much less so. Here, they are using the structure "kind of a", not the structure "a kind of". They want to make the "thank you" seem small and humble.

The simple answer is that "a kind of" very rarely has "a" after it, so it would be "a kind of thankyou" in your example. The more detailed answer is that the word "kinda" is the colloquial way to express "kind of" so you could also say "a kinda thankyou". The reason that you hear that "a" or "uh" sound after is that "kind of" and "kinda" are sometimes pronounced in a mixed together sort of way (kind'v'a).