Sorry to hear about your Dad. I guess the hospital and GP checked the sputum for any bugs. This is important. The CT chest was clear so that is re-assuring.
Try another anti-biotic called Ciprofloxacin
500 mg twice a day for 10 days if he continue to bring up green phlegm. You also need to help him mobilize slowly to keep his muscle bulk going and give him lots of high carbohydrate
and protein diet.
Sometimes in elderly people chest infection
starts off from a virus mainly during the winter and that can knock them off for a while. Just persevere on looking after him.