Rusty chain is on its way out. It will not lose any strength for awhile but the only way is to re galvanize it or replace it. Zinc paint is a pretty good product but it has no abrasion resistance. You will be painting it regularly and IMHO, life's too short. If it's a real nuisance buy a new chain or buy stainless chain.
It's an anchor, think what you do with it? Its a perishable product.
"...Tongue tied and twisted, just an earthbound misfit..."