Air carrier Captain reported an uncommanded movement of a trailing edge flap. Crew referenced QRC and accomplished a no flap landing without incident.

Narrative

Upon reaching the cruise altitude; we conducted a trim check on the aircraft. After an undeterminable amount of time we noticed the aircraft was out of trim" due to a visible right deflection of the control yoke. I made a comment to the First officer that it was odd that we needed to re-trim the aircraft in cruise twice after no speed changes. After another undeterminable amount of time; I noticed the Flap indicator indicated a Flap Skew/Asymmetry of the right side Flaps. The Left Flap indicated "up"; which was in agreement with the Flap handle position of "up"; with the right Flap indicating just shy of 1 degrees. This right Flap low condition explained the yoke deflection due to the autopilot's attempt to compensate for the left rolling tendency. The right Flap had moved Un-commanded in cruise from up to just shy of 1 degrees. After a brief discussion with the First Officer we chose to reference the QRH for Flap Asymmetry. We read through the asymmetry checklist and determined that the Flap was no longer moving further into a skew. We opted to call dispatch through ARINC due to the crew phone not working on both IPads. We asked the dispatcher to connect us with Maintenance Control to use all our available resources and discuss our issue further. Maintenance Control stated to the dispatcher that they believed it was just an indication issue and that we didn't need to run the QRH Flap Asymmetry if we didn't want to; but that it was up to us. We disagreed with that assessment and opted to run the Flap Asymmetry Checklist prior to landing. We briefed the flight attendants of the situation and proceeded to request priority handling with ATC through CPDLC and ACARS to dispatch. We then notified the passengers. We opted for runway XXR "longest runway" and conducted a zero flap landing without incident. We were told by ramp that our gate was occupied for 30 min. We reminded operations that we were a priority handled aircraft and needed a gate without delay; as Airport Rescue and Firefighting was to remain with the aircraft until reaching the gate. Upon arrival at the gate; we were disappointed that there was NO Manager to meet the aircraft. We were met by several Aircraft Maintenance Technicians; who showed me via their iPad; the extensive history of Flap Asymmetry issues on this aircraft. "Known" and well documented issue. I proceeded to the layover hotel only to find that Additional flying was added to my schedule. I contacted crew tracking to inform them that I was not fit for duty for additional flying. I was placed on hold for 8 min. After the hold someone came on the line and said my first name. I asked "who is this?" and they stated "the Chief Pilot." I stated " this is Captain A." It was pretty disrespectful that the Chief Pilot did not call me by Captain; as my hard work and dedication has earned me that title. I informed the Chief Pilot I could not continue and needed to be removed from my flying for that night; and that I'd continue my schedule the next day. He informed me that scheduling would call me back shortly. Scheduling did call back and informed me that I would be rejoining my trip and I was released into 30 hours of rest. Later that evening I received a voicemail from scheduling stating I was going to be removed from my entire trip with a "Missed Trip"; which can lead to disciplinary action and equated to no pay. I stated to both crew scheduling and the duty pilot that I wasn't able to continue flying for the day. Neither scheduling or the Chief Pilot removed me with the proper removal code. I was removed by and placed back on my original schedule by crew scheduling; then subsequently given a full removal with a Missed Trip shortly after; apparently. Which was retaliatory and pilot pushing in nature for not continuing to fly following an inflight aircraft flight control event. After a phone call to Management; they were able to have my schedule recoded. But that did not change the fact that Iwas retaliated and pilot pushed by Crew Scheduling. Cause: I recommend that Maintenance management and Maintenance Control take inflight; flight control malfunctions seriously. Do not advise the crew inflight; with a un-Commanded flight control malfunction that "it's just an indication and that it's not necessary to run the associated QRH procedures" especially with an extensive documented history on the same issue. Scheduling needs to stop retaliating on pilots and pushing them by removing them from their entire 4 day trip or schedule with "Missed Trip" no pay designations; when pilots state they are not fit to fly. Missed trip designations in a pilots schedule and record can lead to disciplinary action and are not separated from other Missed Trip designations. A Missed Trip is a Missed Trip. The lack of professionalism by Maintenance Control; Crew scheduling; Dispatch; Chief Pilot and ZZZ Operations is absolutely frightening. I have never seen an airline portray such a casual lack luster unprofessional attitude with handling a flight and crew with an inflight Un-commanded flight control malfunction."