Some quick searching… I would go with trained specialist, if not, make sure to wear ppe and to use correct equipment, plan really well.
Since the pests become hostile if threatened or cornered, individuals should use extreme caution when confronting raccoons in chimneys. The best way to deal with infestations is to call professional wildlife removal services. Trained specialists eliminate the possibility of injury and disease transmission by humanely tapping the pests and sanitizing all areas affected by infestations.
Only thing I would change after getting rid of raccoon is, use chimney Caps with smaller holes if mice/rats are in area. Mice can enter holes the size of a US dime and rats can enter holes the size of a US quarter.