Contractor is lazy or ignorant.

Flex duct will meet code , but it's not recommended by the vent co. for sure. I'm not positive but I think a damper IS required , but at any rate it's plain stupid not to have one!

Additionally they have just taken away a percentage of your attic venting by using that. Where is the hot air in your attic supposed to go now?

More of a concern is he didn't provide you with what you asked for. Were you charged less than you were quoted because the work was easier nad materials less costly ???

Don't pay the bill and ask him to make how you ordered it. Hold back a percentage until it rains and you can make sure the new vent in the roof doesn't leak.

In our municipality the codes are on line, and you can call and talk to an inspector. You can check the installation instructions on what the hood manufacturer specifies, it would seem a little improbable that they would specify flex ducting (at least VH was clear on that issue). That could have your contractor's actions violating the warranty which gives you some leverage. While it's been a while, I believe our code specified following the range manufacturer's recommendations for certain issues (and hood specs were one of them).

As for safety and performance, if you have only one gravity damper at the hood transition just above the blower, it may flap when there's wind blowing over the top of the stack. The wind creates a partial vacuum that raises the damper and when the wind shifts or stops the damper falls back down. There was a post a few years ago where someone had found this particularly annoying, as well as letting cold air in. Having a damper on the outside vent as well as the usual one in the hood transition seems to alleviate this. Also, outside vents are usually shielded from precipitation and if this is tied into a vertical stack, is it susceptible to rain or snow?

Should have been solid duct and a damper