Uh oh...
If the "paint" is actually calcimine, then get thee to a Benjamin Moore dealer and prime with their Calcimine Re-Coater (Sani-Flat), pray to The Paint Gods, and offer a sacrifice (preferably a can or two of Behr), and maybe it'll stick
If it's "milk paint" (and that can look kind of like a "white-wash"), then rip out the plaster and "re-rock" it or "over-rock" it (put sheetrock right over whats on there now) and go from there (sorry, milk paint sucks)
If it's an old oil-based paint (possible in an old kitchen), latex over oil may fail rather quickly, and then a coat of oil/alkyd based primer (or the calc-re-coat mentioned) may work
If it'd just powdery old (latex) paint, a coat of Zinsser's Gardz may work