"Can we attach flexible piping to the 6" duct"

DANGER. You cannot install flexible pipe for a cooktop exhaust. Flexible duct is prohibited by Building Code. It is a fire hazard. Here is why: the duct must be smooth so that grease particles do not get trapped and cause a fire. If you have grease particles in the crannies of flexible duct above your hood, and your cooking has even the tiniest flare-up, that grease will catch, the fire will whoosh up the duct assisted by the pull of the air flow, and then spread across your walls, and ultimately your house. You may be thinking "this isn't likely for us". Except that according to the Insurance Information Institute, a home fire occurs every 87 seconds in the U.S., and 50% of all home fires are caused by cooking fires. So just use rigid metal duct, and an elbow if you need to turn it in a different direction.

"Will it affect the venting power?"

What will affect the venting power is the 6" duct size you specified. The duct needs to be a 8" or 10" diameter for good air flow to pull up the smoke and grease. People get by on a 6" duct size because their homes already have the 6" duct behind walls so they are stuck with it. But if you are installing new duct - which it sounds like you are - you have the opportunity to install 8" or 10" duct. It does not make much sense to spend money on a new hood, but curtail its air flow from the getgo with a 6" duct.

"induction doesn't cause as much smoke."

Not true. The smoke and grease is a function of what you are cooking, not the energy source. If you are cooking bacon, frying a hamburger, or stir frying, the smoke and grease are the same whether using induction or a gas cooktop. If your family is vegetarian, or you never use the cooktop for frying , then it makes sense to say your cooking does not cause as much smoke, but it's not because of an induction cooktop. I think it's best to budget for smoke and grease, and if you don't often generate it, you can turn the hood fan to a lower speed, but on the occasion you are cooking a smokey item, you have enough ventilation not to set off the smoke alarm.

Not what you asked, but essential measurements:

- width of the hood is ideally 6" wider than the cooktop, so your hood should be 42" wide.

- depth of the hood front-to-back should be 24" in order to cover the front burners. This is where a lot of cabinet hood surrounds fall short. You can get away with a 22" depth, but not less, or you would have spent all the money and effort for a hood that does not even cover your front burners.

- Distance from cooktop to bottom of hood shoud be between 30"-36". Shorter than that and you will have a cramped feeling when cooking. Higher than that and you are giving the smoke and grease too much opportunity to escape.

Flex pipe is against code, because it is a fire hazard. Rigid ducting only.

I mispoke. Can we use the rigid ducting ( two 45 angles, I guess) without affecting quality too much? If we can't, I think we need to go ductless which I don't want to do.

And as far as the 8" duct, I know that is preferable but the pipes behind the wall won't allow for a bigger duct.

Using 2 45 elbows should be fine and not impact performance. Also make sure to have the properly sized cap on the outside termination of the pipe.

"Can we use the rigid ducting ( two 45 angles, I guess) without affecting quality too much? If we can't, I think we need to go ductless which I don't want to do."

While each time the duct turns a corner cuts down the on hood's efficiency, that cannot compare to the alternative you mentioned of having no duct at all to pull the smoke and grease from your cooking. If your only option is to turn two corners, then do it, rather than no duct at all. Make sure your hood is sized wide enough and deep enough as I described above, to help improve the hood's ability to capture the smoke and grease.

@regbob - every time you change the direction of your ductwork, you add resistance and additional pressure to the air exiting your home. That means that your air needs more velocity to make it to the outside. Having said that, many people have elbow turns in their ductwork, and it's fine. It's also less of a problem if the distance from the hood to the outside is not long, which we don't know.

M Miller- you are correct about the elbows adding pressure and resistance but most of the time it comes down to you got to do what you got to do. They said they are on an outside wall so the total duct run will be about as short as you can get.

When you find an exhaust insert you want to use, follow the installation instructions. It will advise you of what is necessary in venting to not void the warranty. No flex duct.

The duct run will be very short. We have 8' ceilings and the hood will be hung on an exterior wall.

Baffle or mesh filter pressure loss will dominate that from a couple of duct bends. Make-up air of some type will be needed to avoid gagging the flow. This may be naturally present, or will require some entry means. See the many MUA-related threads here.