Are there any tools that track and analyze keyword search volume for the Google Play store or the Apple app store?

Ofcourse many tools you have

I use for IOS our ASO Tool - http://asktolik.com/aso and it's free , also popular sensor tower too, for android you have less tools and more can work with google planner tool.

If you intersting learn more i share with you link my ASO course for beginners in udemy - https://www.udemy.com/app-store-optimization-aso-for-ios-no-marketing-2015/?couponCode=ASOGroup9$

There are no tools available which can give you accurate data since neither Apple nor Google give you keyword data in their consoles. However, there are a few tools which can give you guesstimates derived through different ways.

Apple has recently added "Apple Analytics" that provides data on device types and referring sites. They are more likely to add keyword data in future.

My suggest is to check out two tools which may useful for you App Annie and Sensor Tower,

There is a wonderful write up From Amstat News that could be of great value. Amstat News, Statisticians Have Large Role to Play in Web Analytics 1 SEPTEMBER 2011
An example of a web analytics application that will benefit from statistical technology is estimating the value (CPC, or cost-per-click) and volume of a search keyword depending on market, position, and match type—a critical problem for Google and Bing advertisers, as well as publishers. Currently, if you use the Google API to get CPC estimates, Google will return no value more than 50% of the time. This is a classic example of a problem that was addressed by smart engineers and computer scientists, but truly lacks a statistical component—even as simple as naïve Bayes—to provide a CPC estimate for any keyword, even those that are brand new. Statisticians with experience in imputation methods should solve this problem easily and help their companies sell CPC and volume estimates (with confidence intervals, which Google does not offer) for all keywords.