Flavour can mean a kind, variety, or sort.
Flavoured English refers to different types of English e.g. different dialects, or English that is influenced by another language, or accent of some type e.g. Dutch-flavoured, Finnish-flavoured, locally-flavoured, internationally-flavoured... I even found the expression full-flavoured English idiom in English Translation and Classical Reception: Towards a New Literary History
By Stuart Gillespie
Chang's English is described as being "precise and perhaps too accurate" and "perfect" in Chapter 3, and so that would be the flavour of his English - perfect, precise and too accurate, i.e. unnatural, probably too formal, most likely not including contractions and other features of connected speech.
The author never mentions what accent or dialect Chang speaks, and I've always assumed he spoke RP with a Chinese accent, but other readers may interpret perfect, precise and accurate as implying no Chinese accent at all.