Isn’t there a built-in Logic Card for “A webhook is received” that you could add to a Flow if you wanted to trigger it directly? Then you could copy that URL into a Hyperlink tile.
You could even use the special hyperlink syntax to avoid the Hyperlink Tile opening a new window if you wanted to:
Alternatively, the Homey Flows custom tile is open source, so if anyone wants to modify it to support directly controlling a flow, I’m open to that. 