DS has phases when he is constantly stuck in a book, and times when he doesn't seem to read at all.
It's basically a matter of finding the right reading material, and sometimes, getting him started on it.
So when I find something that feels about right for him (right age/interest/difficulty) I might start by reading it TO him at bedtime - and if I get lucky, he will finish it (and all the other books in the series/by the same author) by himself.
I've had a whole thread over on Children's Books asking for suggestions for a child who is in-between HP books but too young for the next one. DS, now 8, is waiting to read The Half Blood Prince (another 6 months to go); he got to read The Order of the Phoenix when he turned 8. The four earlier ones, he read at age 6-7, then had to wait nearly a whole year.
That doesn't stop him from being immersed into HP world. He re-reads the earlier books, listens to the audio-books, watches the movies, role-plays with his friends, ... and I am so pleased that he still has two big books to look forwards to!
For a not quite yet so secure reader, you could consider the Oliver Moon books - also a 'boy at magic school' theme. The Charlie Bone books (Jenny Nimmo) have also often been recommended. Charlie 'ages' a lot less per book than Harry does (Harry gets one year older per book, Charlie only one term, so although the series has 10 books, the story doesn't get very much 'older'). However at 6/7 DS was not interested in them. They caught on recently, at nearly 8.5.
Over all, I have learned to relax when he is in a non-reading phase; knowing that the next reading phase is probably just around the corner. And in the mean time, he can return to his beloved HP world, and every time he re-reads one of the books, or re-listens to an audio-book, he gets something more/different/new from it.
Re Kindle, I would stick to 'real' books for now; and if anything, get him a different e-reader (check your library - they will have e-books for borrowing too). Kindle restricts you to Amazon books, and though they have good choice obv, it will work out a LOT more expensive than getting piles from the library, or from charity shops.