Can a Soldier be chaptered out for wanting to x-fer from a flight company to a maintenance Co if he has a down slip and can't fly?

In short no they can not chapter you for a down slip. Fought this battle both ways in my time as platoon sergeant of a flight company. Flying is a privilege not a requirement. If the soldier is holding a flight slot by MTOE and he is permanently disqualified from flight it is in the chain of command's best interest to fill it with a qualified soldier. When I was serving there were zero slots in the flight company for non-flight Crewchiefs. They were moved to the maintenance company and other candidates are swapped into those positions. Additional duties should not preclude this move. If the company is I that bad of a position that this soldier has 9 additional duties and they do not have a replacement for any of them that is the sign of a bad command team with no forethought or preparation for the future. Anytime a slot came open due to PCS, ETS, or other menial reason the alternate should move up and two new alternates should be found.

With that said if the down slip is temporary the flight company will probably hold onto a soldier. Especially if they are a good Crewchief and leader. This situation is always clear as mud as it is always a case by case situation and the commander has final authority.

Can they chapter him? Maybe, based on more info. A commander doesn't have to authorize a local transfer, he can simply refuse to sign a 4187 transferring the SM and he isn't going anywhere. Now, maybe the SM is really good and being punished for being good. However, there is always more to the story and it is important to see who said what and on what grounds. I wouldn't go to IG yet, as that irritates people sometime. Use the NCO support channel and get a little more feedback. Maybe they can start training others for some extra duties and eventually they have to prepare to lose any individual Soldier. Later based on feedback going to IG may be a really good idea.
I'm not aviation, but if you cannot fly you cannot do you job and there are legal ways to end Soldiers service when they cannot do their job or cannot deploy. The SM probably has a medical profile and based on the condition when appropriate a permanent profile may force a SM into the IDES. Or maybe you have a profile and haven't done an APFT in a long time, which is stalling your PME attendance. In that case a bar to reenlistment would be relatively easy. Those are just two examples on limited info.

It's been a while, but I'm pretty sure that things haven't changed all that much. Especially AR 600-106. It's fairly clear: 1-4d d. "Unit commanders will - (4)Ensure the number of personnel in crewmember flying positions does not exceed the number of authorized nonrated flight
positions documented in TAADS. Excess, overstrength, and dual-slotted personnel are not authorized crewmember flying status"
The idea of "authorized' is pretty clear as well: 2-6. "Medical Qualifications a. Nonrated Army personnel covered by this chapter must meet class III flight physical standards per AR 40–501."
If his flight status is terminated as per para 2-9 c. (4), then keeping him around in a flight company is really up to the Commander. If he wants to eat that slot with someone not qualified to fly, then it's his prerogative and he will have to answer to higher why he chooses to do so, as it begins to impact the overall readiness of his parent organization.
Of course, this is with knowing that which you have indicated. Not having an idea of the MTOE and a lot more than should be circulated on RP, that's the best I can offer.
*Can* they do that? Sure. The CO can pretty much do whatever he thinks his career can handle. Is it advisable? Probably not. It's really up to the unit Standardization Pilot/Instructor and the NCO support channel to make sense of the situation.

I would suggest calling IG and just inquiring about it

Is the Soldier holding/occupying a flight slot on the MTOE/TDA? If so, and he cannot fly due to medical reasons, and the "only" reason the command has to hold him is because he is holding critical positions in the company, seems like the command needs to scrub the formation and look for alternates in each of the additional duties. Once you have trained alternates in each additional duty(AD), slowly wean the Soldier off that AD. Once all the slots are taken care of, then maybe look at moving the Soldier to D Co. At the end of the day, it is the CSM who makes the final decision where the enlisted Soldier goes or stays.

I spent three years in a flight company without flight status. It was my additional duties that made me valuable. As for the chapter, ask IG

They cant chapter the soldier for having a down slip and requesting to be sent back to a delta company. If the soldier cant get back up then at some point a higher up is going to demand they be sent back to a maintenance company anyway.

I've heard of all kinds of threats. The only time it really matters is if its in retaliation for a whistleblower activity, protected communication with Congress, EO or discriminatory matter. Then senior leaders are in deep *&68@. Otherwise, he should document that now and if they actually go through with it, they will likely have had to doctor something to make that happen (w/o knowing anything else about this). And then he can later prove that the chapter was retaliatory in nature.

A good reputation before the confrontation is vital. But yes, even when you are doing the best thing for your branch, unit, or subordinates; pick the right fight with the wrong senior and it can be a career ender. Having said that, if you look out for your branch, your unit, and your subordinates before yourself, and your ducks are dressed and covered, you will not have trouble sleeping later on in life.

The question becomes, Do to the fact that he can no longer fly, does that mean he has lost his qualifications?" In some MOS' if you lose your qualifications to hold the MOS, you can be re-classed or possibly booted. The other thing to ask, if the unit is holding onto the Soldier because they do not want to reassign the additional duties, is the hindering the Soldiers career progression? Additional duties are just that...additional duties. If they have nothing to do with the MOS, then it might be time to talk to the chain of command. Sounds like they don want to strap someone else with the duties.