I don't have a Kindle, but use the Kindle app on a Mac and iPad. For the ebooks I read in Spanish and German, I could find and set up the relevant bilingual dictionary to look up words on the fly, but haven't figured out how to do it for Russian (or if it's possible). My Russian skills are still quite limited, so it may just be that I don't know what to look for. Any tips?
Spanish and German are supported out of the box on Kindle (the dictionaries are provided by Amazon themselves), that's why it's been working for you. You can get Russian to work, too, you just need to install the appropriate dictionary. The Kindle offer is still pretty limited though and some are only English->Russian as far as I remember. 've seen a new one came out last month, maybe give it a shot? I ended up using Smirnitsky that I found online but not on the Kindle store.