Use a wire brush remove as much loose material as possible, then fill and level the area using prepared vinyl cement patch, you can purchase as little as a 16 oz tube or as much as a gallon and it is very easy to apply and smooth. After the patch dries you can apply a sealer. Any home center, such as lowes or Ace Hardware will carry a suitable sealer and will advise you how to apply it.

The flaking/shaling effect that you describe usually occurs with freeze/thaw cycles when moisture has permeated the concrete, frozen (expanded) and thawed. You can trowel on vinyl cement to level out the surface, but it'll be pretty obvious since its color never matches the old concrete. If that's not an issue, then go ahead and use it. If the concrete's not deteriorated too much and you just want to prevent it from deteriorating further--- wash and scrub the concrete with a bleach solution (or commercial cleaner) to remove dirt and mold and let it dry thoroughly. Then brush or roll on liquid concrete sealer (available at most home improvement stores). That should help alleviate moisture penetrating the concrete.