It is quite possible that Starship reentered with its payload door partially open.
The payload door was scheduled to open at T+11:56. At 11:58 a call is heard on the loop, "Pez door is opening" (the door is named after the PEZ candy dispenser).
Two minutes later a call is heard which seems to say, "Pex checkout". Twenty seconds after that we get our first view of the door, which seems to still be closed.

Whether the door had not yet opened in spite of the announcement two and a half minutes earlier that it was opening, or if it had already opened and then closed again during that time is not known.
About two minutes later a shot of the payload bay appeared showing the door apparently cracked open partway.

It's possible that the door is open more than it appears to be from the camera angle, however from all appearances the door at this point is not fully open. However it is also possible that for this first test it was not intended to open the door all the way but just partially.
An interesting result of the (presumably unintentional) rolling of the vehicle was that there was a bit of a light show inside the payload bay as sunlight streamed in through the partially open door.

This six-second clip is shown in real-time not sped up, and seems to show the sunlight being reflected back and forth between the interior walls of the otherwise empty payload bay, creating a constantly changing pattern due to the vehicle's rotation. Interestingly the multiple reflections causes some of the light patterns to move in counter-rotating directions.
The payload door was scheduled to close at T+28:21, sixteen minutes after the scheduled opening. At 28:30 the call came "Pez checkouts complete, door is closing". However after this call the door seemed to remain motionless in the same cracked open position.
The momentary door flex that you referred to happened at 30:18, two minutes after the announcement that the door was closing.

At this time the vehicle was at 224 km, just below its apogee of 234 km, so this flexing was not due to atmospheric effects and was presumably the result of a command to try and unjam the door. After the momentary flex the door became motionless again and appeared to be cracked open a little bit wider. This momentary flexing was the only door motion that was seen in the broadcast.
This was our last view of the door and no more shots of the payload bay were shown for the remainder of the broadcast.
It seems that the announcements on the loop only indicated commands being sent, not whether they were successful. This seemed to be the implication from the statements of the SpaceX commentator later in the webcast when they recapped the tests, stating:
We were also able to demonstrate that the payload door functions, and so those commands were sent, again data review to come and make sure everything performed as expected.
With no other announcements or confirmations from SpaceX it is quite possible that the door remained in its jammed position during reentry. Not that this made much difference, as the vehicle appeared to enter the atmosphere with either partial or total lack of attitude control. However a partially open door would have likely accelerated the breakup as hot gases impinged into the interior of the vehicle. Especially since it looks like the leeward side of the vehicle was facing into the plasma at times during the beginning stages of reentry before the signal was lost.
Based on past experience it is unlikely that the FAA mishap investigation report will go into this level of detail, at least not the public version. So we will probably have to depend on SpaceX providing details of what exactly happened and whether they were able to get the door closed prior to reentry.
EDIT - SpaceX has now stated the following on their website:
While coasting, Starship accomplished several of the flight test’s additional objectives, including the opening and closing of its payload door (aka the pez dispenser)
This seems to imply that the door was successfully closed, but that interpretation also implies that it was successfully opened, which at least based on the camera views was not necessarily the case.
Although it is certainly possible that opening and closing activities took place during periods when views of the payload bay were not being broadcast on the livestream, either by choice or due to the fairly frequent loss of video signal. Attempting to correlate the statement from SpaceX with what we saw on the broadcast is difficult, but perhaps not impossible. Even so it seems that at a minimum they seemed to have had some difficulties either getting the door fully open, fully closed, or both. Whether the door was completely closed by the time of reentry seems to still be something of an open question, which hopefully SpaceX will clarify after they complete their mishap investigation.