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What do you mean by "demonstrated"?  You have some proof of the absence
of first-turn advantage in Chieftain Chess?  Could you perhaps share this
proof?

I am so far unconvinced.  You tell me that you pretty much always win your
Chieftain games, which suggests you have not played against any opponents
that seriously tax you, which in turn suggests that you have no sample
games with high-level play on both sides to use for reference.  But you
also say that you win with an aggressive strategy, which suggests that you
think you can get some advantage by doing something rather than idly
maintaining your position, which suggests that tempos have value (at least,
you are playing as if they do).

Unless you have solved the game or you have a large, high-quality
statistical sample showing that black wins at least as often as white, I'm
not sure how you could demonstrate the absence of a first-turn advantage,
nor does such an absence seem inherently likely to me based either on your
testimony or from reading the rules.

Keep in mind that the first-move advantage in FIDE Chess is thought (at least by Betza) to be approximately the minimum advantage that MASTER level players will notice in practice; I would hazard that no one currently alive is as good at Chieftain Chess as a master-level player is at FIDE, and so it seems plausible to me that you might not easily notice the first-move advantage even if it were LARGER than the one in FIDE.