Well, without plugins, waypoints and anything like that, one solution would be to capture the touch input's coordinates and translate that into scene coordinates (depending on how much of the screen your level takes).
If it's full screen, you wouldn't need to do this transition and could, for example, directly use the coordinates and have the character move on automatic until he reaches them.
Try action Move Towards, tick "ignore vertical" and see what it does.
You also have a vector 2 variant of this action, which might be preferable.
Use a curve action (type curve and see what you get, like curve float which you can synchronize with the beginning of the character's move) to modify the max speed so there's a smooth acceleration. Tweak the curve until it looks neat.
You could even create three states, one of the acceleration at the beginning of the move, one for most of the trip, and one of the deceleration at the end.
The flux would come out of the first state after the character would reach maximum speed (you use a Float Compare to check this FsmFloat max_speed value).
Every time the flux enters a state, use the current post as the "start from" reference. Might require getting the character's current 2D position at the beginning of the state.
in the second state, the middle one, use a finishing distance that makes sense so as to move to the last state which will manage the deceleration.
In the first state (acceleration state), if the character already reaches destination (checked with finishing distance), then go straight to deceleration state (third in the chain) and use the current speed obtained from the first state (that is, the current max_speed value).
Don't insist too much on accel and decel either. The character's displacement has to be smooth but not sluggish either.
