I'm not sure how this "quartering" works it the sentence

Quartering is from heraldry and it means in this context I always imagined the stars in the top L quarter and stripes I the bottom R with the union flag in quarters making up the remaining parts top R and bottom L.

Quartering is when a flag or lozenge or shield or what most think of as a "coat of arms" is made up of several elements, split into four.

With two sources, as Union Jack and Stars and Stripes, one will be repeated top left and bottom right, the other top right and bottom left… very different from the way Australian or New Zealand flags include the Union Jack, even though their jacks are the right size.

If anything, with that design Holmes was implying the UK and US would share the rest of the world equally.