ChimneySaver Water-Based Water Repellent - 5 Gallon Container

Per the manufacturer, it would not work and you can either just repaint the chimney or remove the paint and apply a repellent.

According to ChimneySaver manufacturer instructions, the chimney surface must be clean and free of dirt, dust, stains, efflorescence, and other coatings before application. While pressure washing can be an effective method for cleaning, it is not a mandatory step; the critical requirement is a clean surface at the time of application. If mortar joints have been recently repaired, allow at least 72 hours for them to cure before applying the product. For new masonry, a minimum curing period of 28 days is required. We recommend testing the product on a small, inconspicuous area before treating the entire chimney.

For the ChimneySaver Water-Based Water Repellent - 5 Gallon Container, only one coat is needed for proper application. If applied correctly, a re-coat will not be necessary shortly after the initial process. The product comes with a 10-year warranty, which is based on a single, correct application. Start at the bottom and work your way up, allowing the material to run down over the portion below. If the product is being absorbed quickly, proceed slower. This technique may cause some material to run over flashing or shingles if they are not protected. While it won't harm them, it may appear shiny on flashing. If it gets on shingles, it can make the roof slippery. We recommend using SaverSystems ChimneySaver Pack of Six Protective Sorbent Pads to absorb any runoff. You can use a cheap paintbrush to spread the run-off evenly on the flashing so it does not stand out as drips.

If applied correctly as per the instructions during the initial process, a re-coat will not be necessary that soon.