Flutter - Custom Radio Buttons

Question

I am trying to build a form in my Flutter app and I want to have the user select multiple items, similar to a radio button.

I don't like the way radio buttons look, so I want something more along the lines of a material button like this:

I have tried building this as a list view, but I can't get it to behave like a radio button or a selector button. I have made a few attempts, but I really just want to have a material button look that act like radio buttons. When I submit the form the data within the buttons should transfer through.