It depends how bothered you are on how it looks. When I had chromed bumpers. I kept the backs painted, not with Hammerite, but with etch primer and silver metallic.
The best approach is to remove the bumper, and remove all the flaking and loose finish. Then etch prime and apply a top coat of your choice. If necessary you can then spray over with Dinitrol of equivalent. You might also refurbish the bumper irons at the same time and if you refit with new nuts and bolts it will transform the look.
