Like @amn41 said you probably want to use the REST API function of the Rasa server. I supposed you could utilize the socketio function, but I think using REST from Flutter would be easier to setup.
Basically your app would send the user’s input to that rest endpoint and wait for the rasa sever to respond. you would need to parse the json response and pull the response text and display it in your app.
If you want to see how some of that parsing is done, there’s a really good Web chat ui I’ve played around with and uses HTML / CSS / jQuery. You may not be a fan of jQuery, but it is pretty easy to see how to deal with different response formats from straight text, to panels of data.
It is pretty much plug-n-play locally so you spin up your rasa server and action server (and anything else you need like Duckling, etc) open index.html in a browser and you’re good to go.
That repo is here: