It sounds a lot like what my dad is going through. I think it's LPR, a form of GERD which doesn't involve heartburn but includes the phlegm factor.
My dad is 70 and he goes through the hacking/coughing/vomiting phlegm thing every day, all day long it seems. He has been in absolute misery since this started getting worse about a year or so ago. He is so absolutely depressed about it!
I've been researching it like crazy trying to find some way to help him. He has been to allergists, ENTs, a bunch of different people - just not a GI specialist. I finally forced him to make an appointment and he went to one who will do an endoscopy at the end of this week. I printed out a ton of info about LPR for him to give to his GI doc and the doc just kind of looked at it and didn't really say much. Either the guy doesn't know anything or he is just going by his standard procedure. Either way, if this doc doesn't look into LPR more seriously then I will personally find another GI doc who will take it seriously.
Look up info about LPR and ask your dad if he has the symptoms listed. It's sometimes called "silent reflux" because there's no heartburn involved like there is with regular acid reflux. Some doctors may not know about it because it's a relatively newer diagnosis. But I think it's definitely work checking into because these stupid doctors don't seem to know anything about anything.