According to Amazon (https://kdk.amazon.com/gp/vendor/sign-in?ie=UTF8&origina...), if you are offering active contents that have access to their Whispernet mobile network, unless you are selling your app on a monthly subscription basis, you are limited to use at most 100KB / month for a single user.

There was supposed to be a Kindle app store. Not sure what happened to it.

There are some apps in the normal Kindle store (mostly games), but no separate app store.