Flaking concrete is not a problem that will go away on its own. If fact, it takes fairly aggressive action to stop the flaking (also called scaling or spalling) and save the floor. Spalled concrete is caused by water getting into the concrete, freezing (and expanding) and thawing. Improperly finished concrete is particularly susceptible. Deicers that contain salt can also cause spalling. Another cause is concrete that was allowed to freeze while it was curing. In this case, the concrete would need to be removed and replaced. In the other instances, fortunately, you can resurface the concrete.
Power wash the floor using a rented power washer. You need to remove all of the flaking concrete, as well as any dirt, oil or grease that may have adhered to the floor.
Fill in any depressions caused by the flaking with epoxy mortar, following the manufacturer's directions. Repair any cracks using mortar. Use a trowel to make the repair level with the original floor. Allow the mortar to cure.
Put on safety goggles and protective gloves. Apply an acid wash to the floor to roughen it up so the primer will stick. You can also use a mechanical grinder for this step.
Apply primer to the floor. The primer, essentially a glue, will help the finish to adhere. Use a broom to spread the primer. Bear in mind that most concrete refinishing products must be applied while the primer is still wet.
Mix a batch of polymer-modified cementaceous concrete and pour it over the floor while the primer is still tacky. You can mix a tint into the concrete if you want to match the colour of the original floor or put down another colour. When you select the concrete to use for this process, make sure it has a strength equal to or greater than the original concrete, as measured in psi (pounds per square inch).
Spread the concrete finish over the floor using a squeegee. Use a trowel to detail the edges of the floor. You can use the trowel or a broom to create a finish texture for the floor, or you can leave it smooth.
Allow the finish to cure for 24 hours. At this point, you can add a second coat of polymer-modified cementaceous concrete if you are not satisfied with the floor or if you want a thicker top layer. You may want to add further protection by sealing the floor with a concrete sealer following the manufacturer's directions.