ePub in general doesn't work on a Kindle (you have to convert them to mobi), but you can create your own "Kindle magazines" (don't know their exact name) using calibre.
One use case of that is that you can feed RSS feeds to your calibre's news feature and schedule them to be sent to your @kindle.com email address at a specified day / time of the week. Essentially DYI magazine filled with whatever blogs you want.
That sounds nice! I have a Kobo e-reader, and I use their beta browser or pocket to read this kind of things, but especially the browser is not very convenient.
I've switched from a Kindle to Kobo a few months ago, and it's one of the rare features that I miss. Pocket integration gets me close enough, but Kindle really nailed the magazine approach in my opinion.
On the bright side, Kobo at least makes a distinction between a book and an article, while Kindle just treats everything as a book.