Indeed Flattement is French. Vibrato is Italian. Yet both are used when discussing music, in English.Peter Duggan wrote: fingered vibrato seems a perfectly logical and acceptable term for its use in non-French-speaking trad.
Or German, because Quantz used the term flattement when writing in that language.
However it seems that many English flutists in the 18th and 19th centuries used the term vibrato (or "vibration") to refer specifically to finger vibrato (the only sort many orchestral flutists of the time did).