Bookshop supports local bookstores, but sadly, it seems that you can only read ebooks you buy there on Bookshop’s website or app. You can’t read them on your Kindle. (See Bookshop’s ebook FAQs and this Reddit thread. You can read them on your Android e-reader, however, and apparently Bookshop is working with Kobo to bring its eBooks to those devices. (See I Tried Bookshop.org's New eBooks.)
For more details, refer to Bookshop’s eBook FAQs and How-to-Geek’s Review.
Kobo has an affiliate program that sends a percentage of your ebook purchase to your favorite local bookstore.