Should I +2 again?
I tried you flow, quite interesting. That widget you have there, I am curious where you get that icon. Turns out to be right caret symbol > with some rounded corner background
Yeah, it should be a dedicated button. My test flow usually contains trigger that may not be turn on, but must executed manually during the test.
PS : you can actually share both flow and widget in single xml. When you publish flow/widget, you can select the flow, and select the widget as well.
That single xml will contain both.