Wait – if you touch a Slugma in Pokemon-amie, you burn your hand off.
…So how the hell is Flannery petting them?!

Explanation A: Flannery is so HOT she can touch them without burning her hands.

Explanation B: Then again, if they could burn EVERYTHING they touch they couldn't even go outside without causing massive wildfires everywhere, nor could you throw a Pokeball at them without it melting, so I'm just gonna assume that they CAN be touched and/or trust Flannery enough so they let her pet them.