Wizkids Rules!

While I have Con Artist active, if I name a character and that character's die is in the Prep Area, does adding that die to my roll count as "drawing" the die for the purposes of Con Artist's ability?

If it doesn't and I can't field dice that originated from Prep for free via the ability, what happens when I name say, Flash, have one Flash prepped and then draw another Flash from my bag? Am I able to field either of the two dice for free if they roll character faces? Do I have to keep track of which Flash was which and only field the one that came from the bag for free?

While I have Con Artist active, if I name a character and that character's die is in the Prep Area, does adding that die to my roll count as "drawing" the die for the purposes of Con Artist's ability?

No. “Drawing” means “drawing”—i.e., physically pulling the die from your bag.

If it doesn't and I can't field dice that originated from Prep for free via the ability, what happens when I name say, Flash, have one Flash prepped and then draw another Flash from my bag? Am I able to field either of the two dice for free if they roll character faces? Do I have to keep track of which Flash was which and only field the one that came from the bag for free?

If you name a character that has a die in your prep area, and you happen to also draw a second die of that character from your bag during the Clear and Draw Step, you may field for free either or both of that character’s two dice this turn if you roll a character face. There is no need to track which die is which.

The relevant text from the card is as follows:

Constantine – Con Artist:

While Constantine is active, you may name a character before you draw. If you draw and roll that character this turn, you may field it for free.

-The Dice Masters Rules Team