Short answer: No.
In the FreeGameDevWiki you can find an up-to-date list of web services of FOSS music (CC:BY and CC:BY-SA).
Of those, the only one I am familiar with is Jamendo, and while it does offer something called “radios”, I do not think that you can exclude non-FOSS music from them (all music is CC, but CC:BY and CC:BY-SA are definitely not the only licenses used).
By the way, although the UI suggest that you can only search music with a certain license, you can use the following Jamendo URL to browse both CC:BY and CC:BY-SA at the same time: https://www.jamendo.com/en/search?qs=fq=license_cc:%28-nd%20AND%20-nc%29
I suggest that you download whatever you like and play it locally.
About donations, check the remaining sites. I would certainly discourage you from donating to Jamendo, as they are basically using FOSS because they saw an opportunity there, they do not seem to care much about the FOSS philosophy.