That is irresponsible of your builder and is a warning sign about their knowledge, quality and integrity. Reduction from 8" to 6" alone is a problem. It will reduce air flow and so the effectiveness of your hood and it will increase hood noise as well as the amount of electricity used. So increased cost, more noise, less odor, gas combustion by-products and other effluent removal. Flex duct creates two problems; It's a major fire hazard and it increases static pressure (reduces air flow). From a static pressure standpoint 6" flex is roughly the same as 4" rigid in most installations. At a MINIMUM you should have 8" rigid for your entire run if that is what your hood calls for (Many US hoods undersize this). If you have many bends then you should increase that to 10" to keep static pressure down.

"Have you thought of changing the wall studs to 2x6" rather than 2x4"?" I don't wish to destroy the wall on the far side. I have a large map wallpapered to the other side. I could build out with a false wall for some additional distance, but I don't see that as necessary since I can do at least 3-1/2"x14" (almost equivalent to a 8" round duct). Plus, I found a standard "Straight Register Boot" to transition to 8" diameter. I believe 3-1/2x14" equates to about .05 friction loss for five feet). I just don't know what 2200-2500 FPM will equate to in sound level at the hood. I foresee cutting a 4x15 opening (or bigger), at the back of the hood. I am re-reading rjpjnk's post and I remind you I only have five straight feet till it feeds straight into the fan venturi. I found this is an engineering handbook: Duct velocity should be between 1500 and 4000 FPM  Hood velocities (not less than 50 FPM over face area between hood and cooking surface)  Wall Type - 80 CFM/ft2  Island Type - 125 CFM/ft2  Extend hood beyond cook surface 0.4 x distance between hood and cooking surface Filters  Select ï¬lter velocity between 100 - 400 FPM  Determine number of ï¬lters required from a manufacturerÂs data (usually 2 CFM exhaust for each sq. in. of ï¬lter area maximum)  Install filters at 45 - 60°to horizontal, never horizontal Using this as a guide I think an average 400 CFM for general-purpose venting @ 1500 FPM means that I am well covered with a variable speed 1000 CFM external fan and 8" duct area. I'm guessing that at 1500 FPM it will be pretty quiet. The old Vent-a-Hood units are supposed to deliver 300 CFM each and I usually only use one. They are super noisy at near my ear level and 18 inches away. The air passes through a 3-1/2" x 4-1/2" rectangular opening! That's small and seems to equate to almost 3000 FPM! I guess it's no wonder they're so noisy... Am I missing anything? Bad calculations or asumptions?

The OP wrote: "So...I’d love the size of a larger range and a larger hood just for “style”..." Few want a larger hood for style; most resist having a larger hood even though it increases effectiveness at the cost of more required air flow rate and potentially a deliberate means of supplying make-up air. Cooking plumes expand as they rise, hence the hood capture aperture has to be larger than the area occupied by whatever pans might be used on the cooking surface. Otherwise, the effluent partially spreads into the kitchen allowing grease and moisture to settle on surfaces, and odor to spread and linger. A six-inch wider hood helps achieve this. A large enough front-to-back dimension is also needed. Assume the plumes expand at an angle of about 10 degrees from the vertical. The hot cooking plumes will have an upward velocity that depends on cooking surface temperatures and presence or not of gas combustion products. When these plumes (to the extent that they are captured by a large enough hood) reach the hood filter, they will bounce off due to conservation of momentum unless the air velocity induced at the filter by the hood blower is high enough. Commercial and residential practice suggest a value of 90 ft/min at the hood entry aperture (not the filter) is sufficient to retain the effluent and achieve containment. 90 ft/min is equivalent to 90 CFM per square foot of hood entry aperture. Use of induction cooking without any searing or wokking or hot frying may allow a lower value, but not below 60 ft/min. Hood blowers can only meet their specified zero pressure loss flow rate when hanging in free air. All other configurations have pressure loss (air flow resistance) as a function of flow rate, and thus when installed each blower flows less than its rated value. Buying a blower rated around 1.5 times that needed for containment (see above) should overcome the likely pressure losses, assuming there is a make-up air path suitable for the flow rate.

Ah! you missed one of the versions of a comment I have added to quite a few threads. Here it is again. Because we do not get to close off parts of the hood not receiving cooking plume impact, all of the hood has to flow the amount needed at the most stressing part of the effluent plume to be contained at the hood baffle space. How much do we need? Well the actual issue is what velocity of air has to be pulled past the baffles to ensure that the rising plume is pulled into the baffles and contained, versus reflecting off of the baffles and potentially curling back into the room, thereby escaping the capture area and hence removal by the hood. Hot cooking plumes over gas burners can rise at velocities of 1.2 m/s, or almost 4 ft/s. The baffle gap is roughly half the baffle assembly area, so to entrain the plume flow, it seems that some portion of 4 ft/s or 4 x 60 CFM per sq. ft. of baffle area is needed for good containment. Actually, there is usually space under the baffles larger than the baffles proper, so adequate flow is needed all across the hood capture aperture. I believe that I have about 900 actual CFM at home, pulled through a 10 sq. ft. Wolf Pro Island hood. This is equivalent to 90 ft/s. This works over induction hobs, including searing and wok cooking with a 3500W Cooktek wok hob. As it happens, Greenheck also looked into the requirements for CFM, perhaps like me doubting that 100 CFM per ft. of hood edge had a mathematical connection to the process of cooking plume containment. They have published a range of values, and I have taken the liberty of copying their relevant table below. So take your hood area, multiply by some value you believe in for actual needed flow, then multiply by another factor to account for blower ratings not actually applying to the conditions in which they are used. (Another topic written about here more than a few times.) http://www.greenheck.com/media/pdf/otherinfo/KVSApplDesign_catalog.pdf No one has complained here that aiming for 90 CFM/sq. ft. of hood aperture allowed smoke and steam to escape into the kitchen, so long as the hood overlapped the cooking area by enough to capture the expanding plumes.