What type of pipe is best for venting my stove hood? Does flexy hose work or should it be hard pipe only?
According to IRC, the duct must be made from galvanized steel, stainless steel or copper. It must have a smooth interior, and be air tight. Which means you're not going to want to use a flexible product for this application, especially that flexible plastic crap. Instead, you'll want to use rigid duct like this.
And you'll want to make sure you seal all seams with mastic or tape, that's designed for the purpose.
If you're not sure what building code is used in your area, the safest bet is to simply follow the installation instructions provided by the manufacturer of the range hood.
International Residential Code 2012
Chapter 15 Exhaust Systems
Section M1503 Range Hoods
M1503.1 General. Range hoods shall discharge to the outdoors through a single-wall duct. The duct serving the hood shall have a smooth interior surface, shall be air tight, shall be equipped with a back-draft damper, and shall be independent of all other exhaust systems. Ducts serving range hoods shall not terminate in an attic or crawl space or areas inside the building.
M1503.2 Duct material. Single-wall ducts serving range hoods shall be constructed of galvanized steel, stainless steel or copper.
Best is sticking with rigid ducting that is the same size as the output of your stove hood, with as little elbows/direction changes in the shortest distance possible. Make sure the size is rated (or overrated) for the output of your hood - minimum you want is 6", and that's just for a 300-400CFM hood.
If you can choose, given the same distance, go up instead of sideways. Heat wants to go up already. You can get 3.75" x 10" ducting that can go in the wall where a 6" round duct will not fit.
Flexible ducting has a drawback that it will accumulate grease in a greater amount and shorter timeframe than smooth walled rigid ducting. All those little ridges are places grease will adhere to, which increases the risk of a bad fire in case you ever get anything going up there (which, in a typical residential application might be slim chance).
Hard pipe is recommended because it will work much better and is unlikely to be crushed or compromised.