Guys, we all agree that at such a low speed the priority is to stop it from decaying and eventually recover some. Without thrust the only thing to do is to reduce drag. Retracting flaps is definitely reducing drag, but this is only effective when you don't create more drag somewhere else (ie by increasing the AoA...).
In terms of drag reduction retracting flaps might be a good thing, but totally irrelevant when you simultaneously let the AP add more drag by increasing the AoA trying to follow a wrong flight path.
To answer WojtekSz's question, the first thing to do when you realize you have no more available thrust is to recover and maintain the best gliding speed, which you won't achieve through flap retraction. In other words the PF should take manual control, control speed and eventually call the PNF for flap reduction.
WojtekSz, can you tell me why according to you the AP shouldn't have been disconnected before selecting flaps 25? Why maintaining the ILS all this time? To me the AP just spoiled all the benefits of the flap reduction which induced even more drag as the AP had to correct a slight deviation below GP induced by the flap reduction.
What was Sully's first action when he lost both engines? Take manual control or aircraft reconfiguration?