If it were me I would abandon the old ducting and remove it.

Because this is a vent duct I would go back with aluminum flexible duct 10" you can find it at Home Depot. No need to insulate it -- it's vent only.

I wouldn't use any elbows the vent duct is flexible (bendable) but I would avoid bending it if possible. Try to keep it straight as possible, and terminate it so the air is expelled out thru the roof.

If you need more than one length of pipe a good quality duct tape can be used to seal the joints.

Thank you! Unfortunately- there is no option to vent through the roof- there is an upper level to the house over the kitchen. There is a possibility of venting it directly out the back- going through a small ‘attic’ area over the enclosed back porch. What kind of vent would be best for the outside of the house? 10” round seems gigantic.😅

Start out at 10" then transition down to 7" or so last few feet or so, use a 10" to 7" reducer. This will require you to find 7" vent duct to complete the run. How long is this run?

10" to 7" reducer

Keep in mind that if you don't do this properly you may have problems.

Like if you do a lot of greasy cooking at some point in the future it may start dripping oil / grease. If humidity is high and venting is horizontal for long distances can cause condensation traps that eventually may leak / drip.

It's best to keep this run short, straight and as vertical as possible and exhaust it to the roof. Other wise you may have more trouble to contend with.

How are you using this fan? Keep in mind if you increase the resistance the fan will be louder as well.