What the phrase is expressing is, "Choose what's truly your favourite flavour".
Can I say, "Choose your true, new flavour"?
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Gramatically that's correct, but always think if the opposite makes sense.
Choose your false, old flavour
The true is absolutely unclear as to what it means - what does it mean a flavor is true? It's nowhere near implying "truly favorite". It could be interpreted as "real flavor of X" instead of an artificial substitute maybe, but that's stretching it.
This is a little confusing, because "new" doesn't appear in your definition of "What the phrase is expressing". I'm going to assume that what you meant to say was "Choose what's truly your favourite new flavour."
"Choose your true, new flavour" won't work.
In the first place, "true, new flavour", with the comma, means in English syntax
Choose your flavour which is true and new.
Without the comma it's still not what you want: that means
Choose your new flavour which is true.
Your fundamental problem is that the only word your catchphrase supplies which carries any (forgive me) flavour of "favourite" is your. That is what, according to your definition, you want true to modify, and you express that this way:
Choose the new flavour which is truly yours.