There isn’t a way to do this directly from flutter right now although that may change at some point – see this bug/feature request. You do have a couple of options though.
The first is to use MethodChannels and simply write the android code you want to create a background service (or if you want it to always be a background service you can probably do that without needing communication from the flutter side).
The second is some combination of these two plugins – android_alarm_manager and android_intent. But that won’t help for all use-cases.
EDIT Feb 2021:
Flutter now supports running background processes. See this page for details.