Acute or chronic bronchitis can result in shortness of breath and swollen ankles and feet. The swollen ankles and feet are a sign of right-sided heart failure. Yet, he might well have bronchitis and, at the same time, a different cause of shortness of breath and swelling of the ankles and feet. To sort out the causes and effects of these relationships will, in all likelihood, require consultation with a lung specialist, also called a pulmonologist. One should not simply assume that bronchitis is the cause of the other two conditions. It is not uncommon for a person to experience an increase in cough and sputum production, sometimes for a year or more, after smoking cessation. Furthermore, the excess sputum may be difficult for him to completely expel, resulting in low blood oxygen levels which would contribute to both the swelling and his shortness of breath and lead to heart failure. One of the first things that should be done is a chest x-ray and determination of his blood oxygen level.
Your father should consult with a physician, familiar with chronic lung disease and right-sided heart failure, but also acutely aware of other causes of his symptoms such as congestive heart failure and blood clots to the lung.
If he hasn't already, he should go to a pulmonary doctor, not just his regular Primary Care doctor- could be lots of things-