I think you might be confused about how we use the word "compression". I believe the term refers to when you are flying so fast that the pressure on the structure is too great for the control surfaces to react against...in-game it means when you're flying fast and discover you can't control the plane. Your controls "lock up" and it's almost impossible to change direction.
When you deploy flaps you extend the rear edges of your wings and tilt them downwards. (Extend them while you're on the ground and look out your side window and you'll see what I mean.) This gives your plane more lift, allowing you to stay in the air at slower speeds without fear of stalling, and it also allows your plane to turn tighter than it normally would. The downside is that you also create more drag, which may cause your plane to slow down.
With flaps out your stall warning will go on a lot sooner if you pull back on the stick, or if you try to maneuver, or in level flight if you are slowing down too quickly. What you're experiencing is not compression, it's called 'buffeting' I think. That's when your plane starts to shake as you approach stall speed.
I suggest you read the section on flight dynamics in the trainers website. It will explain the physics involved when you fly, and why things like stalls, spins and compression happen.