So, I might be over a decade late but since this thread was made I think a couple choices have come out that match up really nicely with Storm Kindler/Master of Storms.
First would be an Oracle with the Ascetic mystery, since it gives you both the levels in Spellcasting needed to become a Storm Kindler and the unarmed strike damage of a Monk with the same level as your Oracle level (1d10 if you go 10 Monk/10 Storm Kindler), to increase the damage of your Storm Shape without any multiclassing required, and as a bonus you can pick the Elemental Imbalance curse both to get some lighting themed spells for extra flavour and to gain Levitate as a bonus spell at the 5th level which allows you to take ranks in Fly earlier and qualify to become a Storm Kindler as soon as possible.
And secondly you could use the variant rules for multiclassing from Pathfinder Unchained to multiclass as a Monk and be able to inflict 2d8+5d6 damage to anything caught in your storm shape by the 18th level regardless of which class you pick, but you would be giving up half your feats for it