Here's how the adjustable 90' duct looks

Yes, there are various HVAC companies and HVAC distributors that can build custom duct parts, although the distributors providing such services generally expect a HVAC tech to have designed the interface. Total Air Supply in NH is an example. You will have to hunt down the appropriate companies near you. For your purposes, a sheet metal shop that would more typically deal in stainless steel assemblies may be a better choice. This all depends on your intentions for finishing the area.

Conceptually, you might imagine a large stainless steel hood extension (box) that has a base area equal to the top of the hood and a height that reaches the ceiling. Clearly, a hole at the bottom to connect to the hood, and a hole at the back to connect to the wall duct would provide an air path. What one would actually want inside this box might be a sheet metal assembly that smoothly directed the air from one aperture to the other for minimum turbulence and grease precipitation.

The starter duct at the top of the hood may have to be removed or shortened. A damper has to be in the path somewhere.

Smaller boxes can also work, the above was only an example, but in this case I would go for more massive. If you are not a mechanical designer or know of a friendly one, you will have to hire someone.

kas

Having a foot and a half of flexible metal pipe at this diameter will offer only trivially more flow resistance than a multiply jointed elbow. Make your life easy, and just use a short piece of flex duct to make the transition, keeping the curve as smooth as possible, use either aluminum or stainless flex duct. Flex ducting exacts a price in air flow over distance both because the surface isn't smooth and it tends to wander, introducing additional turns. In this case it's not much worse than the jointed elbow for flow, and may be easier to provide a smooth route.

I have the impression that flexible duct is against code because it is more likely to trap grease and cause a fire.

Don't use aluminum ducting for ducts that can potentially host grease fires. The risk may be modest but it is not necessary to incur the risk.

kas

Thanks for all of the input. Just to provide some additional info...we live in So Cal and most of the time we have the kitchen windows open, so I don't anticipate using the hood very often. Also, we eat extremely healthy and I can count on one hand how many times/year we ever use grease or oil when cooking. Lastly, we have an adjustable chimney that will attach to the top of the hood so it will hide everything behind it.

It sounds like my options are 1) custom made rigid duct, or 2) aluminum or stainless flex duct, being aware that it may not be compliant with code and could trap grease.

Should of removed the 2x4 stude and framed a support. Just use flex at this point.

Jdoe2 points out the critical need when starting a kitchen reno to plan everything from the beginning. This takes time and aggravation, but saves it later.

Delete aluminum from option 2.

kas

It seems to me I remember seeing a piece of duct like the 90* you show that allowed for rotation of the pieces at each of the joints like shown in the picture. With something like this, and perhaps two of them, you could rotate it around to fit. Or look at two 45*s.

Any sheet metal shop can make you a box with 2 holes that match perfectly. You basically want a tiny version of an HVAC plenum. I'd slope the bottom of the box back towards the vent hood just in case any condensation gathers in there. Just call around your local area.

I could post a bad blunder of a customer of mine who's kitchen installer makes this guys look like perfectionist. But I will always point out to my customers that the smallest details make the biggest difference. It could be worse. Have the hole be recentered. Did you pay for a half assed install or a professional one.