"You adjust the flaps to point the nose of the aircraft upwards....

"You adjust the flaps to point the nose of the aircraft upwards. All other things being equal, the plane slows down."

Wrong. The reaction of extending flaps is the nose pitches upwards so forward trim is required. Aircraft need to slow down to extend flaps, that is achieved by thrust reduction, then flaps are extended. The resultant drag slows the aircraft further if thrust is not increased or rate of descent is increased. The later is rarely used as flaps are generally extended in the lower altitudes and high sink rates are not desired.

"The point is to use some of the airflow over the wings to recharge the batteries,"

You have corrected yourself and now say the windmilling props could generate electricity, that maybe the case, the amount is debatable.