Ideally, you start with enough aperture to capture the rising expanding effluent. Then, having the aperture defined, calculate the CFM necessary to achieve a velocity equal to the rising effluent velocity. This would require 180 CFM per square foot of aperture for 3 ft/s rising effluent if there weren't other considerations. One of those is that with baffles, that velocity only needs to be achieved over about half the area due to the aero shape of the baffles and the flow around them. I didn't figure this out from computational fluid dynamics, but from the behavior of my Wolf Pro Island hood dealing with my induction wok which is offset towards one side (the induction cooktop is offset toward the other side). I expect mesh filters to behave similarly due to the mesh blocking at least half the area of the filter. While a fairly poor analog, if one thinks of the effluent as billiard balls in a zero gravity field hitting the hood filter, one can appreciate that conservation of momentum will cause those hitting a flat surface to bounce away from it such that the angle of exit equals the mirror image of the angle of arrival relative to the perpendicular to the surface that the effluent hits (just like light). The need is to change the momentum of the reflection by entraining the effluent into the hood air flow. Ideally, this is done as the effluent reaches the baffles/mesh and there is little bouncing reflection going on. You may appreciate that the flat surfaces of your nominal hood where there is no mesh will be regions where there will be effluent reflection. Some of that will be captured by the air flow which pulls in from a range of angles. In any case, for best operation, one wants the actual hood aperture to encompass all of the rising effluent and not make the aperture smaller just to get the local air velocity up. (A commercial kitchen hood is an example what is relatively optimal for maximizing capture while minimizing the cost of air handling.) But the bigger the hood, the more CFM needed, and the more make-up air CFM that has to replace the air in the kitchen. This not only adds the modest cost of ducting in MUA, but significant cost if the MUA has to be pushed by a fan and the fan has to be controlled to keep the house pressure in a narrow range. This can be more complex in some ways than large commercial buildings which can run MUA continuously and use pressure differential across a damper to control whether the fan output just circulates around in the fan loop or is pushed into the building. I think my previous post suggested that for the hood aperture you have, the actual CFM achieved will probably be enough. But imperfect capture and containment should expected from the hood aperture design due to the flat areas not being capture areas. kas

Find a local sheet metal shop and have them make you a new box that is insulated on the INSIDE. You will need accurate measurements of the outside dimensions and a measurement of the location of the opening where it connects to the air handler. From there you can install the box and cut any holes to connect sheet metal boots to transition to the flex duct. Any home improvement store will carry the sheet metal boots and flex duct. Make sure the inner part of the flex duct is securely duct taped to the metal boots at both ends and the outer layer is sealed with lagre zip ties.

The transition from round to rectangular or reverse can cause rather extreme static pressure. The shorter the transition the greater the SP problem you'll encounter. Make sure to get a proper calc on your full run for exactly how it will be built (including MUA and the hood+baffles itself) and look at the impact on the fan curve for whatever blower you're using. You could easily find yourself with only 200 CFM of exhaust and a lot of air movement noise. Once you're happy with the design and calculated performance then make sure it's installed properly. A surprising number of HVAC people do not understand the impact of static pressure on blower performance.

Love your cabinets! There are two types of units: recirculating (mentioned above) which runs the air through a filter. They don't work very well. All exhaust hoods are vented. They have to be. They run the air through a filter, through a duct (or directly through the wall) and outside. That is why you can smell coffee and fried chicken when you walk past a restaurant! The duct can run up through the ceiling or out the back. There are also (less efficient) downdraft models which run out through the floor or wall (down below). Some older homes vented into the attic, but that is generally no longer allowed (imagine your attic full of years of grease). The capacity of the hood is measured in CFM (cubic feet/minute). The more powerful ones also require makeup air - air coming in to replace the air being sucked out. It's not cheap because it needs to be heated/cooled. Some units can be converted from recirculating to exhaust. Where is your kitchen designer? All this should have been dealt with long ago - before the wall was closed in.