There are not "flavors" as such. There are just 3 types of Beans - regular, shiny and rainbow.
The regular ones are fairly plain, whatever the color it makes no difference - red is the same as yellow/blue/green etc.
Shiny have a few lighter patches on them, hopefully it should be obvious. They increase affection a little bit more than regular Beans.
The rainbow ones are by far the best (they are also more rare). Obviously they're the ones with rainbow stripes on them (they'll be last in the list of beans, scroll across to get them). It only takes 2-3 rainbow beans to completely max out a Pokemon's affection.