While I agree with you that the 1768 Warrant does not refer to the colors of coats directly, it is in the same language and form as the 1751 Warrant which refers to "...the following Regulations for the Colours, Clothing, etc. ...". George III followed his grandfather's example and started the wording of his Warrant the same way. So I infer that when George III states in the 1768 Warrant "The King's or first Colour shall be the Great Union throughout..." He's also saying that the uniforms shall follow the same scheme as 1751 unless noted otherwise. The second Colour(flag) was to match the facings of the uniform which were laid out for each regiment in the 1751 Warrant.
The "Great Union" of course refers to flag of "Great Britain" the Union Jack Flag which was formed by joining the flag of England (Cross of St. George--white field with red horizontal by diagonal cross) and the Flag of Scotland (Cross of St. Andrew--blue field with diagonal white cross.)
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