I'm not even sure I think there is a typical flute tone.
I'd suggest that you follow your instinct and make it sound appropriate.
I mean that sincerely.
Perhaps if you describe the type of flute, the song it is performing, and your opinion of what your raw recording sounds like, some folks will dare to suggest a presumption but I personally feel that you are fully qualified to make a subjective choice such as this.
Think in terms of "woody", "pure", "clean", "breathy", "dark", "airy"... and work in the direction that suits the material.
My guess is that a collection of tunes by any single flautist and flute can be treated each, individually, to help convey the intent of the performer.
Trust your self to use the "you'll know what you like when you hear it" approach on this phase of the production process.
all the best,
mike