This is a "Fowler" flap!!!(and a 737 flap)
Probably not, getting the sequensing right would be a real headache, making sure the fore flap and aft flap extend and retract with respect to the midflap would just be too hard. You need to see how Boeing have done it, it's not pretty. They have sorted it out somewhat on the 737-6, 7, 8, and 900 by doing away with the foreflap and a new arrangment to actuate the aft flap,