I think you will need to as this question on the Android Developer discussions Galaxy Watch4 is an Android device. I don’t believe that the older Tizen versions of Galaxy Watch support Flutter.
I have been building and deploying to a standard Galaxy Watch, with no issues. I asked a question about Flutter on Tizen previously (Flutter on Tizen), the repository was marked as an official Samsung one.
I apologize, I ran into the Flutter documentation while looking for something else soon after replying to you and forgot to update this. I know even less about the Flame game engine. If no one helps you can try opening a support request. They have ties to the Tizen Studio Development team and they may know.