If you are looking for varieties that flower more frequently, I would advise steering clear of commercial varieties, and either growing potatoes from true seed (TPS) yourself, or trying varieties from hobby breeders.
There are two factors that lead the majority of commercial varieties to not flower. One is virus buildup - this may result in affecting the plants, preventing flowers.
The second is a genetic bottleneck having to do with the "T" cytoplasm. Nearly all commercial potatoes are the result of inbreeding for the past 150+ years, predominantly from one potato. This document is one that Tom Wagner has referred to.
http://www.plantsciences.ucdavis.edu...potsum1rd.html
The image below is one attempt at describing the history of potato cultivation and relationship between different wild and domesticated species.
