It appears that if you have the camera in AUTO mode, you can not do what you want.
If you are in MANUAL mode, and you have the flash off and then turn the camera off, the Camera will remember.
See chart on page 238 in the camera User Manual.
Recently I bought a Canon 870, I would like to know whether it is possible to keep flash always turned off. After turning the flash off and when I switch the camera off, after turning the camera on, the flash is again turned on.
I am not sure whether it is possible to change the settings for the above.
Any help is highly helpful.