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. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well. If this post solves your problem please help others find this answer by clicking "Accept as Solution.".
Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X