Well this flag is a new one.. it's mixes the flag of the Cromwells with its Scottish & English shield and the flag of white, green and red means the White as liberty, Green as fertility of the land and red means the republic built over blood
But that's a rather anachronistic way of creating flags.
Flags of that time are based on the colours and designs of national or prominent arms and saints banners.
Tricolours became popular due to the success of the republican Dutch and later even more republican French.
The meaning of the colours were essentially post facto. Ante facto the Dutch tricolour was the colours of the Prince of Orange, the French was the Parisian banner with an added white stripe.
If the British Republic is emulating both Cromwell and the Netherlands then I could see a colour altered Dutch tricolour with a shield rather than then French one you show but even then green is unlikely to be chosen.
Otherwise I'd assume a flag of English and Scottish quarters; perhaps bearing whatever symbol the republican forces are using - whether that's the arms of their leader or whatever.