Does anyone have good experience getting app reviews for iOS and Kindle? I have several hundred downloads on both markets, but no reviews so far.

In comparison on Android I have 6 reviews for my full version and 9 for my free version. The Android version has been out about a month longer than Kindle and iOS, but I'm surprised I haven't gotten a single review in those markets.

Currently, once the user passes level 6 (out of 95 levels) the game adds a button on the main menu asking them to review. Are there better methods to solicit good reviews?

Most have a pop up (ie native pop up) which displays every so often, usually after so many completions or time based.

This usually says :

"Enjoying this app? Please support us by rating it on the app store"

With the buttons :

"Rate now!" , "no thanks"

If you search the forums and shared code are you will find examples of this.

Since I added code like that I have gotten 5 reviews in my first 7 Days.

I think the popup is important. I have rate buttons in my game OmniBlaster, but I can't tell that anyone has ever rated it.