Maybe focusing on non-fire moves for now would help. Vulpix are able to learn a pretty nice spread of moves so perhaps until yours can gain a bit more confidence and less fear, try teaching some dark, psychic or ghost type moves.
If you want, I could send a few TMs your way, as a way to make up for the inconvenience.
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If you want, I could send a few TMs your way, as a way to make up for the inconvenience.