I believe you can 3d print a metal mobius strip as the entrance to a rocket stove, and do away with the chimney. In a pressure cooker under heat, if there is a small opening in the shape of a mobius strip, the outside of the pressure cooker is cold, a very thin layer. The outside of the stove with a mobius strip entrance would be cold, and right beyond it is hot, outside the stove (actually a pressure cooker doesn't need a mobius strip hole, as just outside a pressure cooker it's cold, as can be tested in placing a pressure cooker in cold sink water and feeling right next to the stove, it's cold. But a stove is not under pressure. However, a pressure cooker with a mobius strip hole under the weight, right next to the pressure cooker would instead be under high pressure outside the stove, so a pressure cooker like that would tend to concentrate air. I think that analogy holds). The hot air will try to work to get past the cold, so that the outside of the stove, further past the cold layer (or further past the high pressure layer), is hot, but it can't, so it creates a strong draft into the stove, thus air always goes into the stove, and it would never need a chimney.
Also, in an air conditioner compressor, a single small hole in the coils, the hole shaped like a mobius strip, hot air would gravitate TO the air conditioner from inside the house through the ductwork, so that you wouldn't need a blower, and the air conditioner would work better because the vortices produced in sucking the hot air in the room towards it would be vortexed. If the hole is a mobius srip, there is no distinction between the inside of the stove and the outside, since there is only one side to a mobius strip, as the ribbon is twisted once, as you go around, you end up at the same place you started, but you also travel on the other side, as a disc with a hole in it, travelling around the disc, you can't get to the other side.
The only thing, I don't know if the hole needs a weight on it, like a pressure cooker's weight, so that it operates under the "concentrating pressure" idea, rather than just having a cool layer on the outside of the stove. I don't think it needs a weight, but I believe it needs something in addition to the hole that makes the stove be perceived as a pressure cooker. But I think the fact that there is no chimney, automatically makes the air flowing into the stove, have to work against the natural pressure, so any air that flows in, becomes pressurised, and air just on the outside is not cold, but pressurised, so it doesn't need a weight. I didn't come up with all of this myself, but I did see a device that relied on Tesla's spinning motor generator that somebody made recently. Combining these ideas, the outside of the stove would have to be insulated, rather than the inside, as the outside of the stove would get incredibly hot. Also, the air conditioning coils would not need to be compressed, if the outside of the coils were wrapped in insulation, no motor or refrigerant needed. The air that gets sucked towards the insulated coils would be concentrated or compressed. The only thing missing is perhaps the release of pressure part. I think the air conditioner or stove would need a weight on it like a pressure cooker's weight, because that would mean that the inside of the coils or stove would be marginally at higher pressure than the outside, so that it would work as a virtual motor or compressor. So I would have to say, that the hole doesn't need a mobius strip, but the entrance is an L shape. So perhaps your existing stove, the entrance can be capped off. On top of the chimney, put a weight on it like a pressure cooker's weight (doesn't need to be a mobius strip shape to the chimney's exit). Also, for an air conditioner, it would operate as usual, but a chimney would go up to the roof, and have a weight on the exit, and the blower can be turned off. So, no change to the rocket stove at all, other than closing the entrance, and putting a pressure cooker's weight on the top of the chimney.
I wouldn't read any of that stuff above. What I think would work, is to cap off the stove's entrance, and cap off the chimney as well. But at the top of the chimney, the design is like a pressure cooker that chemists use. At the top of the chimney, capped off, it's like an air lock. You have a metal flat disc, attached to a spring. On top of the chimney, the outside is threaded. You screw down a cap over, which makes contact with the spring. But there are -TWO- holes on the sides of the cap. When you tighten down the cap, it puts the spring under pressure (the disc inside the chimney would have to be supported by an annular disc that's welded to the inside of the chimney so that when the cap is screwed down over the screw, it has something to screw down over). But by chance air can flow out through the threads (highly vortexed air inside the stove and not high pressure because the stove is not under pressure, it's sucking air into the stove through the chimney's exit), and leave through the two holes on the side of the cap which is screwed over the threads, the threads being on the outside of the stove. That means that most of the time, air is not leaving (or entering), but oscillating the inside disc. I think it's exactly like this: https://www.youtube.com/watch?v=gnDox0P01hI&t=2s, but perhaps the orientation on everything is reversed, so that the threads are on the inside of the chimney, the movable plate attached to the spring is on the outside, and the two holes are on the nut screwed down from inside of the chimney, the nut pushing onto the spring, and the movable plate is on the outside on top of the chimney. Also, I don't think you need a chimney, but an insulated box, insulated on the inside, as a stove, with the entrance or hole in the house by the fire. The nut would be screwed down on the inside, so the oscillating plate is vibrating on the outside of the stove by the entrance. That would make it appear that the air outside of stove in the room is like high pressure autoclave air, and the air inside of the stove is reversed. So I will revise it again. I think what you need is a solid nut that screws down from the inside of the stove, onto a spring, onto a plate on the outside of the stove, onto a solid disc with a hole in it, so the plate can screw down onto something. Then that means only highly vortexed air can enter the stove past the threads, and it's so efficient that it wouldn't need a chimney. And you wouldn't need two holes on a solid nut.
It's pretty unclear how exactly you think this will work. Can you draw a picture? If you can't, is it actually possible to have a hole shaped like a mobius strip? I don't think so, or else you mean something other than what I understand you to be saying.