I've often considered buying a kindle specifically in order to read foreign language books.
There is a feature of potential use which is the built-in dictionary .... highlight a word and get instant look-up - if you have a built-in dictionary for the language of the book you are reading that is.
However, as far as I know, such dictionaries only exist for the "big" languages:
German, French, Spanish, maybe Italian (into English, that is).
I don't think there is one for Welsh<=>English (but if there is, I will be very pleased to hear it).
Note that I'm not talking about just a normal E<->W dictionary that you can read as a book on the Kindle, but one that will enable the all-important highlight-a-word then look-it-up feature, which requires that it be built especially for the kindle.
Once upon a time, I asked Bangor University (specifically the department who produced Ap Geiriaduron) if they might one day produce a kindle-enabled W<->E dictionary, but I didn't get a reply to my email.
However, Steve's tips sound very useful, even without a built-in lookup feature.
I suppose another way is to find a Welsh-language author that you like and see if they have produced any books that are available on Kindle.