I gunned a Panzer IV Flak flying a YAK9T armed with a 37mm canon. After taking out the turret I was not able to follow up on destroying the Flak, even after multiple 37mm gun hits
First, when it comes to questions of gameplay like this, Youtube and similar videos are not the best choice. It's better to present the raw .ahf film that allows a better examination.
This is getting obvious when Icome to your question: "Why didn'tI get the kill?"
My question to you is: What do you mean by that? Was the Wirbelwind killed by someone else and you only did get an assist and now you are wondering why? Or was the Wirbel still up when you landed, and you are just asking why you weren't able to blow him up? From the .ahf film I could have seen the whole situation.
Now if it's been case 1 (someone else got credit for the kill) - It's the one doing the most damage to the target that is getting the kill credit. If another tank finally killed the Wirbel by shooting the hull, most of the time he will get the kill credit.
If it's been case 2 (why did I smoke the turret only, and why did he not blow up): The Yak-9t is no tank buster. It's firing HE shells, not AP. It's well suited to kill light vehicles, or disable the open (!) turret of a Wirbelwind, but it has a very hard time to penetrate the main armor of a real tank. For that, take a Hurri D, Il-2 or B-25H(which also has HE, but the shell is simply big enough).