If you can see this(?)from the basement,it has some depth to it.You may find yourself openning up a can of worms.IE;multiple coats of paint(u need to paint more than three coats),this unknown(?) material falling from the wall because of the moisture or weight from the paint,thefinished paint job looking worse than the old wall itself due to uneven adhesion or adsorption of new paint.There are more variables involved ,however ,I can't speculate any further without seeing what kind of wall covering is on your kitchen wall.

The easy solution is to first buy a primer that is good for both alkyd and latex,and apply that first(very important step).Then paint your choise of covering over the primer.

FYI...I used to work in a paint factory and I am now and have been a general contractor for over ten years