@crispius I use a Kobo rather than a Kindle, but I have several friends who read Libby books from the Winnipeg Public Library on Kindles. This is the WPL's help info about it https://help.libbyapp.com/en-us/6027.htm. Does your Library seem to think it isn't possible?
Libby is the APP owned by Overdrive. You can borrow straight from your Kobo anywhere. In the US (only) they will send books to your kindle but I'm not sure how that works … (Kindles don't sideload, right?)