There is nothing to stop you from downloading the Kindle app and the Kobo app onto any/all of your devices. Each app is designed for you to be able to read books in a suitable format.
However, ereaders Kindle and Kobo are, as Blossoming says, tied to different formats and one cannot read books in the format meant for the other. Kobo has a larger range of books available but Amazon has a pretty good range of books too.
Ereaders are specifically designed for just reading although also have audio books available.
Despite having multiple devices to choose from, I always have my Kindle with me as well. I can read in bed at night and not disturb DH, I can also read in bright sunlight, sitting in the garden, it is a comfortable fit in my hand (easier than a real book). The battery life is better than any of my other devices. I'm not too worried about buying books from Amazon, it's the story I care about! I haven't tried a Kobo but there are plenty of reviews available if you carry out an internet search.