Patient.co.uk recommends that a person with pneumonia be clinically recovered and no longer infectious before flying. A doctor can advise whether a patient is fit enough to fly.
Cabins in modern aircraft are pressurized to an equivalent of 5,000 to 8,000 feet above sea level. The lower barometric pressure is not a problem for healthy individuals, but it can create issues for anyone who has reduced lung capacity from pneumonia. An individual who is breathless while at rest would want supplemental oxygen while flying. Fluid in the lungs or sinuses can expand, creating pressure and discomfort, the New York Times notes, and swelling or pain from injuries or illness may worsen from air pressure changes.