Probably one of the longest lasting gum flavors I have tried lately is the Dentyne Ice brand. This gum advertises on the package that after chewing it for at least twenty minutes your breath will be fresh for at least 45 minutes!
The gum flavor indeed does last a long time! Even after chewing the gum for 30 minutes there is still flavor coming out. And not only do you get flavor while chewing the gum your breath does actually stay pretty fresh for a decent period of time.
There is not guarantee that this gum flavor lasts the longest, but it does last a long time! Try it!