Kindle doesn't have apps. The only other option would be a service that automatically adds PDFs for you by emailing them to your kindle address.
e-ink Kindles do have (limited) apps. I have a weather app and can play chess, mahjong, and soduku on my 3rd gen e-ink Kindle at home.
This has been removed from the more recent Kindles, since the Kindle Voyage at least.
Can confirm, java inside. Outdated, 1.4 or something like that last time i touched it.
Instapaper actually does this. You can have it e-mail everything you've added to Instapaper to your Kindle as a kind of personally curated newspaper. It's not well publicized but is relatively easy to configure in your Instapaper account.
Wouldn't you be able to do this with the daily email digest on IFTTT too?
I've found the Instapaper Kindle export to not include article images. Very frustrating and devs don't seem to care (and probably care even less now with being bought up).
Yes, when it occurs it totally breaks the experience of reading long reads on the kindle. This, and the fact that multi-pages articles are sometimes not properly fetched.
I'm working on generating perfect (all images, all pages) .mobi periodical files from rss feeds, send me a mail (in my profile) if you want to test a MVP when it is ready.