So, new character is a Pyromaniac Gnome, who just happens to wield a Great Sword. She gets Produce Flame 1/day (actually twice with a trait). How would you rule this interacts with the great sword? Understandably, she wouldn't be able to throw or touch with the flame when actually wielding the weapon, but since switching from/to 2-handed wielding to/from simply holding the sword in one hand are free actions, it would stand to reason that when she isn't 'wielding', she'd be able to fling fire. Now, what isn't ruled is what happens to the flame when that hand is holding an item (wielding the sword).
1) Does grabbing an item with a hand under the effect of Produce Flame cause the flame to extinguish? I see no rule that states this would be the case.
2) Does the flame continue to emit light when wielding a weapon or holding an object with that hand, or is the flame concealed in the closed hand, only to burst back to life when the hand is reopened?
It doesn't harm you or your equipment. It isn't a touch spell, so isn't discharged if you touch something else. I can't find a flaw so far.
As it's in the palm of your hand I'd say concealed in the closed hand - or maybe just dimmed to the equivalent of candle light as it glows around the edges of your fingers.