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.

If you can install a remote "in-line" blower, a fan motor that sits not in the rangehood but somewhere in the duct that goes to the outside, usually at the far end of the duct, say in the attic just inside the opening to the outside, you should look at this website: Fantech.net. They have a line of in-line motors, and you might find one that will work for you. They have one that can be installed in a 6" duct, and its cfm is about 480. If you need more than that, get one that can be put into the rectangular duct you described.

Any blower that is not positive displacement (like an air compressor piston) has what is called a fan curve (see below). This curve relates flow rate to pressure drop across the blower. If duct length pressure loss plus hood filter pressure loss plus make-up air pressure loss uses up much of the pressure capability of the blower, flow rate will drop quite a bit. But there is hope because depending on relative characteristics, a supplemental blower in the duct path or externally wherever the duct exits will share some of the pressure drop, causing the flow rate to rise to where is hoped to be. Now, the air flow has to be the same through both blowers, so their respective fan curves have to be consulted and blowers tuned, perhaps, to work well together. This solution is better applied when an inadequate installation already exists. The easier approach is to buy a better blower (higher pressure loss capable blower) and use it instead as a single blower. Overall, the solution is situational and not amenable to glib advice.Example fan curve.

"The manufacturers of Vent Hoods are miseducating the consumers." Yes. Somewhat. Not really. They are in business to make money and they do that by making hoods as inexpensively as possible and then selling as many as they can for as much money as they can. Their goal is NOT your health or the IAQ of your home - that is up to you. Telling consumers that they'll also need to spend money on MUA if they buy hood X will negatively impact their sales (ignorant consumer will just go buy a hood from brand Y instead because it doesn't say you need MUA even though it has an identical need for MUA) so they do not want to do that. MUA is also not something that fits well within consumer hood manufacturers world except to the extent that they might offer a hood w/ integrated front curtain ducting. It is much more of a pure HVAC thing. It can be supplied to the return ducts of an HVAC system, the supply ducts or ducted directly to appropriate locations. Incoming air can be heated by gas, electric or hydronic. Incoming air may need to be humidified or dehumidified. It often needs to be electrically integrated with the HVAC system controllers to function properly. Consumer hood manufacturers - ARE NOT IAQ or HVAC people or engineers - they make something decorative that by nature must include air movement so they reluctantly include air movement in their product. Commercial hood manufacturers - ARE IAQ and HVAC people and engineers. Their customers are much more educated than consumers. The one singular purpose of the product they are selling is IAQ - so they design and sell systems that provide good IAQ. Aesthetics is quite secondary for them. Residential HVAC companies in the U.S. - ARE NOT IAQ people (they should be though). A tiny few, less than about 1%, know it well and a few more know it a very little but the vast majority know just enough, based on what they've been told at a 4 hr CEU course, to sound like they know what they're talking about but they don't really understand it. Most residential HVAC people do not understand air movement or why things are done the way they are - they only know how to use tables that tell them to do this or that and as soon as something is outside of defined parameters they're totally lost (though sometimes don't even realize that they're lost). Licensed Professional Engineers do (or most do, some don't) understand air movement and other elements. They are the people who create the tables that HVAC people use. They can think independently. Defined parameters for them are not tables but the physics of air - it's movement, temperature and components. Unfortunately, most U.S. engineers do not have a good understanding of human physiology (except perhaps for biomedical engineers). They do not, for instance, understand how CO2 functions in our bodies and how high levels of CO2 due to poor ventilation affect us. Or how poor ventilation resulting in high levels of VOC's, PM, Carcinogens and Pathogens affect us.