Just google "pocket to kindle"
There is no real "integration" (as in built-in apps for a service) on Kindle device itself (like there is Goodreads integration) for none of those "read later" services like Pocket/Instapaper/Readability/... BUT for most of them there is ability for wireless send & deliver article or articles as a book to your Kindle.
Each Kindle registered to Amazon account gets unique e-mail adress that is used for wireless delivery of books/personal documents to that Kindle. That e-mail address is the gateway for "integration" between Kindle and the content on Pocket and the like.
I'm not using Pocket but I've used Instapaper in the past and I know that it has ability to periodically send all unread articles to your Kindle.
So you keep using Pocket and extensions and apps you used to add articles to your Pocket account, now you just need to add to the mix a way (usually some web app like
https://p2k.co ) to periodically sent new content to your Kindle e-mail address.
Those types of services/web apps usually create "kindle periodicals" type of mobi book, magazine-like with multiple articles as one book, were Kindle also keeps past issues of a magazine.