Do flaming deal extra damage from a lance on a charge?
1d6 to 2d6 or 3d6 with spirited charge.
I would say only the weapon damage gets doubled (tripled) since to my knowledge nothing i can find appears to boost the damage dealt by elemental weapons in that manner. That being said most abilities call out that they prohibit the damage from being increased so while i would rule no off the cuff your GM might rule differently.
EDIT: Belay that found this quote "Multiplying Damage
Sometimes you multiply damage by some factor, such as on a critical hit. Roll the damage (with all modifiers) multiple times and total the results.
Note: When you multiply damage more than once, each multiplier works off the original, unmultiplied damage. So if you are asked to double the damage twice, the end result is three times the normal damage.
Exception: Extra damage dice over and above a weapon’s normal damage are never multiplied."
The bolded answers the question here.
When mounted and using the charge action, you deal double damage with a melee weapon (or triple damage with a lance).
The feat is not specifying where the damage that gets multiplied comes from only that it does it when using a melee weapon.
I'm guessing that you are correct and that you're the rule would apply here.
I would like to hear from others as well.
If this is how it works then flaming and stuff like that are pretty crappy on charge builds and only weapon size and static damage are good to improve.
As my primary PFS character is a cannonballer cavalry halfling, I had to research this early on, and what Talonhawke quoted is correct. You never multiply additional dice onto a sneak attack. Yes that means you can't do extra elemental damage. But you should be doing triple damage already, so why do you really need to munchkin game for that bit extra? Snag a ghost touch, keen lance, and call it a day, thats enough to drop any CR relevant major baddie in a single hit if you are a cavalier with all the damage boosting feats like power attack anyway, in most cases. My cavalier's static damage on a charge is somewhere around +69 at level 10. 90 or so if i challenge first...