Would this not be smart to do because you may come in a little fast, therefore the flaps would send you back up? Or would you absolutely want flaps in this situation
Flaps steepen the descent angle - in other words, you run the risk of falling short of the runway. So in a glide you keep the flaps up until you can be certain of making the landing point. Once the landing is guaranteed, you can then deploy gear as well as flap to slow down as much as possible - being aware that these actions will further reduce the gliding range, so constant reevaluation is required.
That would be up to the discretion of the flight crew, what forced landing site they selected, approach route, etc. Typically deployment of flaps in a forced landing scenario will only be done once the airplane is guaranteed to make the landing site by gliding in that landing configuration.
You would certainly prefer to have flaps available in order to reduce landing speed. If so, the pilot in command has discretion whether using flaps is appropriate to the situation. Unfortunately, the loss of all engines may prevent flaps from being deployable. In two of the most famous airline no-engine landings I can think of, the Gimli Glider and Air Transat Flight 236, flaps could not be used due to lack of hydraulics.
In the case of US Airways Flight 1549, however, the APU was used to provide hydraulic pressure (which was impossible in the other flights mentioned, since there was no fuel left in those cases). Partial flaps were used in the ditching.
Yes flaps would be used when landing the 737 with the loss of double engine failure. A double engine failure landing is an Emergency Procedure. Intentionally landing flaps-up with a double engine failure creates an unnessary Second Emergency.
A double engine failure flaps-up stopping distance may exceed runway length & the speed limits of the tires.
The Airbus flap system is electrical only.
The Boeing 737 flap system is normally hydraulically operated. In the event of a Double-Engine failure, the 737 flaps can be extended electrically.
A 737 double engine failure landing is similar to a screwed-up parachute landing...there are no do-overs.