The action I use for this is called "Touch Object Event". In the case of a flappy-bird style game, you'd create an invisible gameobject with a box collider that's the size of your entire screen. Target that full-screen gameobject with the "Touch Object Event" action, and then send whatever events you'd like.
For example, when the full-screen gameobject receives "touch began", send an event that moves the FSM to a new state, where you use other actions to move the bird upwards by X.