What are possible complications of a chronic infection in the sinus because of a perforation from a root canal?

See Endodontist. It depends upon what was placed into your sinus. If it was the disinfecting solution the denist uses to clean your canals then the sinus usually recovers with no intervention. However, if the 'filling material' of the root canal was placed in the sinus then you need the help of an oral surgeon or ent. Since you said this is 'chronic' I would suggest getting this looked at soon.
Oral surgeon or ENT. If this has been awhile then go back to the dentist that did the root canal or go see a specialist like an oral surgeon or an ent. You may need to get a procedure named a caldwell luc or kind of a sinus cleaning out or scraping. That usually solves the problem.