Don't forget that for each pet swap, you lose a turn. Yes, conflagrate will deal double damage on burning pets, but if you need 2 roudns (swap + conflagrate) to deal it, it's just as if you had done 2 normal attacks with any other pets.
If you want to do something in those lines, get a Tiny Snowman and two Kun Lai Runts. Keep Blizzard up and abuse of Deep Freeze. At least you'll be stunning your opponent, making him lose a turn as well. Deep Freeze damage is pretty awesome too, and the two Runts have another ability that deals extra damage if target is stunned, so depending if the other guy tends to swap pets when stunned or not, you can either swap too and stun his next pet again, or keep your Runt there and deal very high damage.