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cantonCoord = v.vTexCoord + v.vTexCoordFlag * zoomFactor;
A general formula would be
int2 FlagsPerRowAndColumn = ...; // (16,16), (10,4), or (10,2)
cantonCoord = v.TexCoord + v.vTexCoordFlag / FlagsPerRowAndColmun;
For regular flags, FlagPerRowAndColumn is always (16,16) so your zoomFactor of (1/15,1/15) is quite close, but but custom flags, I have implemented, for a personal mod, a function that returns (10,4) or (10,2) — Vanilla values — which could be useful for your PixelShaderFlagTextColorColony::main.
I know that the texture coordinates of the pattern are treated by the shader as they would be for any regular flags, but I think that the symbol is just another layer, added after the masked flag and before the overlay.