You can use the Roku app on a cell phone for remote listening and use bluetooth earphones on that.
Roku Community Streaming Expert I am not a Roku employee, only a user like you. Do not ask me support questions via private message -- post them publicly to the Community where others may benefit as well.
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Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X | Streaming Stick 3600