Summary: Just be consistent with yourself, not with anything or anyone else.
This question contains a false premise: that there are two sets of non-overlapping spellings, one from the United States and the the other from the United Kingdom.
In actual fact, it is far more complicated than that. Each individual word, or sometimes each set of morphologically tail-similar words, works in its own way, with individual preference varying on both sides of the Atlantic.
For example, just because this or that American writer of renown happens to use grey rather than gray, or signalled instead of signaled, or amoeba instead of ameba, this does not mean they are using “the British spelling”.
By the same token, an Oxford don who uses emphasizes instead of emphasises, or fetus instead of foetus, or acknowledgment instead of acknowledgement, is not using “the American spelling”.
And not just for one reason alone, either. In nearly all such sets of spelling variants, it is possible — indeed in most cases perfectly easy — to find examples of native speakers naturally using spellings that Microsoft Word castigates them for as being from the wrong side of the pond. This is complete nonsense.
So long as a variant exists, it is not “wrong”, and it is unreasonable to brand it as such. Many words in English admit more than one spelling. True, today these number many fewer than compared with before the printing press, but it is not like one variant is “correct” and another “incorrect”. Certainly if a respected dictionary lists both variants, none should gainsay you, least of all some prescriptive spelling checker that does not believe in the same word having more than one possible spelling.
The important thing is that you be consistent to your own choices within the same piece of writing, as seeing the same word spelled different ways in different places by the same writer in the same document looks haphazard, capricious, and even careless. So don’t write both grey and gray in the same document (unless it occurs in a proper name), or both signalled and signaled. Choose one and stick with it.