What are verbs for phlegm? For example, what is the verb to describe the action of blowing out the phlegm from throat? Or the verb to describe someone has or generates phlegm in one's throat?
To add to the verbs above, there's also "hawk" which can be used, although it might fall under the remit of 'slang'
To clear or attempt to clear the throat by or as if by coughing up phlegm.
To clear the throat of (phlegm).
An audible effort to clear the throat by expelling phlegm.
As James Webster said, coughs up could be used:
Force (something, especially blood) out of the lungs or throat by coughing
You can also use the verb expectorate:
Cough or spit out (phlegm) from the throat or lungs
One usually "coughs up" phlegm.
v.intr To expel air from the lungs suddenly and noisily, often to keep the respiratory passages free of irritating material.
v.tr. To expel by coughing
As others have suggested, "cough up" is a standard term now. For an older or more formal term, you might try: