Why is deploying speed brakes not recommended with the flaps extended?
https://www.eucass.eu/doi/EUCASS2017-318.pdf

Above shows a configuration where the flaps and spoilers are deployed. The blue line shows the vertical velocity of the wing's wake, which is indicative of the lift being generated. Since the effect of the flaps lessens outboard, that causes the downforce shown above near the end of the wing due to the spoilers.

Since spoilers are thin and are allowed to move/flex slightly under aero loads, and since this downforce is far out with a greater moment arm, any slight [asymmetric] disturbance to any outboard spoiler panel will result in a roll, when compared to:


Smaller flaps deflection: since the inboard part of the wing creates less lift (less flaps), the slope (lift to downforce) will be shallower, which lessens the impact of an outboard disturbance.
Speed-brakes are used on their own: there will be a uniform downforce distribution over the wing without the abrupt shift from lift to downforce shown above.


Note that the manual says may and slight. Do not expect a huge roll, just anticipate if it happens, the FBW is not programmed to correct it unless an input is made.



I found the same recommendation in the FCTM of the 747-400 and 737 (all variants). It's flaps 5 and 15 respectively. They don't state the reason, but buffeting was mentioned.


  The use of speedbrakes with flaps extended should be avoided, if possible. With flaps 15 or greater, the speedbrakes should be retracted (737 FCTM).


@kevin also pointed out in the comments that the 777 explicitly states there is no issue with using the S/B in landing configuration, which to me sounds like extra care was taken with the FBW or spoiler design.

Another possible reason is to lessen the load on the actuators of the spoiler panels, with the flaps deployed that's a lot of suction behind them, but that doesn't answer the rolling part.