I would discipline it. Time outs are a bit vague at one, but you can try and see if they work.
My third, now two, was an angry LOUD screamer, starting around 12-14 months, especially in quiet public settings! Literally, the minute we stepped into a grocery store, library, Target, restaurant, she was SCREAMING. I disciplined at home with one warning, and then a consequence, not angry, just methodical after warning. She curbed it right away at home, but not in public. In public, my uncle, father of 10 awesome kids, recommended the pinch since you can't give a swat on the hand or bottom in public. The first time I did it, after one calm warning, she was so furious, she screamed even louder of course. She may even have done it one or two more times (she was way tougher than my other two in every way). The third time, she started to scream, caught herself, and leaned away from me with a look like, "OK, I'm not screaming." and so I gave her all kinds of praise and hugs. That was it. She no longer did the screaming past age 15 months. People lose their minds over physical discipline, but I have to take all my kids on all my errands and I couldn't just "wait out" the screaming phases or "leave them home".
To clarify, I ONLY disciplined the purposeful "screaming" knowing she understood my warning, and was in control of the behavior. I never disciplined real emotions or crying from fatigue or hunger or sadness or boo boos.
If you're home alone with him and no pressure, and you can just let him do it, then you could wait for the phase to pass by walking away and things that may sink in eventually, etc. If you choose to ignore, it's totally up to him how long he thinks it's fun to do this, and he may spin it into full tantrum mode a bit early if he gets enough practice. Try time outs, but I would step it up if they have no effect. You can see by his behavior that he knows what he's doing and he does understand you dont' like it. Give him credit, he will understand effective discipline. The earlier he learns to control his voice at certain times the less work you have later.