At what speed(s) and throttle settings is this happening? 2-3 is usually smoother than the 1-2 shift as there is less torque multiplication difference. If this happens on a closed-throttle 2-3 upshift, you might check the rear axle for the source of the noise.
On our '66 Newport 383 2bbl, we discovered that at about 25mph in 3rd, that a quick throttle pedal movement, as in cruise . . . no throttle . . . then throttle to maintain speed (about 30mph, or perhaps a bit higher), a "clunk" could be heard from the rear end. The old-line Chrysler service manager at the local dealer said that was normal and not to worry about it. This was when the car had about 40K miles on it or so. No problems ever, from that issue.
On our car, the front u-joint was the first to cause issues. I had first noticed a quiver when cruising at 70mph. As it was not major, just something to notice as my arm was on the top of the front seat back during long highway runs at 70mph, it was not a big deal. Then, a lower-frequency quiver started to happen on brisk acceleration from stop, plus a similar speed-related squeaking. I took the wheel covers off to check for the squeak, to no avail.
So I took it to the local Chrysler dealer (away at college). The service writer drove it a short distance and came back with the diagnosis "front u-joint". It had not been that long since we checked them on the rack at an oil change, BUT that fixed it. The front joint is where most of the up and down movement usually happens, plus driving torque (which can wear the related front yoke bushing and seal), it seems. The rear joint is still the OEM production unit.
Just some experiences,
CBODY67