69 Charger 440 4bbl 727 trans. Not just an idle out of adjustment, but almost a rotational vibration. Damper looks good. ??

Does it just do this while idling?

I bought a '72 Charger in AZ. back in the 80's with a 400 2-bbl that had a vibration at all RPM's. I sold the car to a customer before we ever got it figured out, but several guys were saying they thought it was the flex plate.

That's what I was thinking but wanted someone else to say it.

Is this something that just recently started? Or is this a fresh build?

Just started

If it has good oil pressure and isn't making any knocking sounds, then pop the inspection cover off of the bellhousing and bump the engine over so you can look at the flexplate. It may have cracked.
I'd also verify that the balancer hasn't slipped the outer ring.

What is good oil pressure??

On the balancer. You can run it up to TDC on #1 and see where the mark is.

Depends on what oil pump is on it. If it has a stock pump, then probably 15 psi or so at hot idle and 40+ at speed.
A high volume pump will be at least 20 psi hot idle and 60+ at speed. Of course this can vary if someone has messed w/ the relief spring and/or bearing clearances.

Checking your timing is another way to easily see if they balancer has slipped. If the timing light is telling you the timing is different now than where you previously set it...it's time to get #1 at true TDC and verify the timing mark.

Unless the poster has a newer cast crank external balanced engine a slipped internal balanced engines balancer will not cause a vibration.

Yes, unless it's slipped BAD and is about to come apart/fall off. I mean like the outer ring is wobbling...but he did say it looks OK though didn't he? So yeah, the damper shouldn't be the issue if it's neutral balance.

Unless there's an issue w/ the flexplate or torque converter, it's gonna be time to tear into the motor.

Simple firing order error?

Is there a miss, have you looked under the valve covers.... lifter popped out? Miss adjusted valves/preload?

How old is the gas? I'd drain the tank and put fresh gas in it before tearing into anything.

I put STA-BIL in my tank over the winter one year. When I took the car out of storage the engine had a noticeable vibration to it. Surprisingly, a fresh tank of gas fixed it.

The damper looks fine and the timing is rock solid where ever I set it. I'm hoping the bolts that tie the plate to the torque converter are lose. Easy fix. Other wise