No, flexible ducting is dangerous for kitchen exhaust. The grease will get caught in the nooks and crannies, and can cause a fire. In my area, Code doesn't permit flexible ducting for kitchen exhaust or for laundry exhaust. What caliber of contractor do you have? Not only is he denying the well-known problem of flexible ducting, but he ignored your "discussion" of rigid ducting. When you say "discussed", how firm were you? You need to make him re-do it. Though I think you'd be much safer to find a different contractor to re-do it--it's not worth it to risk shoddy workmanship for ducting in your home.

When you re-do it, it is best to install duct that is 8" or 10" diameter. Sometimes there isn't room in pre-existing construction, but usually 8" diameter can be squeezed in. Smaller ducts will decrease the efficiency of your hood, and increase its noise, especially if you have a 700 cfm hood.

I believe you do need a damper, otherwise how will you prevent incoming air (cold in winter, hot in summer) from coming into your home.

You could also post this question on the Gardenweb Appliances Forum. There are several exhaust/ductwork experts there.

Here is a link that might be useful: Gardenweb's Appliances Forum

thanks akchicago
I will post there too.

As AKchicago wrote, flex duct is not permissable. Additionally, I would want to know what existing duct they tied it into and whether THAT is allowable. Finally, did someone calculate whether the run through the attic (length, turns, etc.) reduces the effectiveness of the vent? You may need a booster.