How can I reduce or eliminate flaking from a limestone basement?
Solution to painted areas - wait for them to flake off, or else wirebrush them with a sufficiently coarse wirebrush to remove the paint. Once they have all flaked off or been removed, insulate the exterior of the foundation to below your local frostline (MN, probably deep) with either spray closed-cell polyurethane or a combination of that and rigid XPS sheets, to minimize the freeze/thaw cycles the stone is subjected to (and save some money on heating, too.) As suggested in my comment, seasonal freeze/thaw cycles are probably to blame for the flaking. Salt (wicking in and drying in place) may be another culprit.

GSA on Limestone: Characteristics, Uses And Problems