Yeah definitions are tricky. If you saw a house consumed with fire, you might look at the circumstances and conclude that it was likely the offspring of the fire that consumed the house across the street, but there wouldn't be anything about the fire's phenotype that would help you come to that conclusion.

If the flames carried the characteristic shape of their parents fire, and they could be distinguished as not the offspring of some other fire by their features alone, then I'd be arguing that fire is alive.

I feel like I'm at risk of classifying certain periodic crystals as alive here, but they wouldn't meet the thermodynamic requirements that I have in mind (which fire does meet).