Yes try and find out what is causing the paint to flake off. Rising damp? Worse near the bottom of the wall? Any sign of a leaking roof? water entering the wall at the top? Is there a visible damp coarse layer?
Is the soil level outside the wall higher than the floor level? If so, water is entering the wall from outside and the new paint will eventually also come off. Fix that before you go further, or, accept that you will have to redo the painting in the future.
Was the surface powdery when you started cleaning it up? Fine hair cracks in plaster can be painted over after filling in any bad ones as already suggested.
If you decide to go ahead with the painting, remove as much as possible of the loose stuff and powder, do what other have already said you should do and then paint on the primer, more than one coat and very important allow to dry properly between coats. Don't be in a hurry even if SWAMBO puts plenty of pressure on you.