This is a concern I never thought I'd have to be wary of-cell phones catching fire. Yes, it seems this is a possibility. However, the reasons why these phones have burst into flames is usually because someone did the wrong thing with them.
Charging a phone that had gotten wet and the battery swelled.
Sleeping with the phone under a pillow and the phone (battery) over-heats
Puncturing the phone
Charging with off brand charging cables
Phone fires are all about the batteries.