Personally I use a combination of Brief (RSS plugin for firefox) and Firefox Sync. Brief tracks feeds as live bookmarks, which are synched between computers by Firefox. I have one folder of ‘home feeds’ that are too long-form for me to read at work in good conscience, and a folder of ‘work feeds’ that let me follow tech news at work. Additionally I have bookmark folders like ‘read later’ and ‘watch later’ for individual articles and videos that I want to spend more time with, again synched automatically by Firefox.
I’m not sure if this setup would seamlessly support a single feed folder that you want to follow at multiple locations, but even if it doesn’t, perhaps it could be tweaked to do so.