How does deploying flaps change the gradient and rate of descent?
Yes you’re viewing it the wrong way.  Deployment of flaps changes all sorts of flight parameters, not just one.  The wing area may increase, the camber and angle of incidence of the wing increase and so the engine thrust line is effectively tilted downwards.  The aspect ratio changes, as does the relative angle of the horizontal stabiliser.  The net result is that the flight efficiency is reduced (i.e. the amount of energy required to maintain height increases) but the stall speed is reduced.  There’s a lot happening and you have to take it all into account.  Typically on approach you’ll want a low airspeed and relatively high rate of descent but without compromising control authority, so the flap layout is designed to provide this.