Why do (some) aircraft shake at low speeds with flaps, slats extended?
There are many phenomena which can cause vibrations. Without knowing further details like the frequency, starting moment or the weather conditions on landing it is difficult say. Common causes are:

Stall buffet/ self induced turbulence Normally when a plane lands it flies with low velocity and a high lift coefficient, near to stall. The flow detaches much earlier and there is more turbulence behind the main wing. The tailplane has to fly through this turbulent zone and hence you feel the vibrations. Sometimes deploying the spoilers, even if you're not flying at stall speed is enough to create turbulence which will hit the tailplane. T-tail airplanes are less affected because they're further away from the air zone influenced by the main wing.

Atmospheric turbulence Can be created due to thermals (in that case it should be sunny) or wind hitting ground structures. If you have landed a couple of times and always felt the vibration it probably isn't the answer.

Wake turbulence Shouldn't be your case either, separation minima exist to avoid this problem and it would probably feel different every time you land.