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“fluency” in Latin

The English word fluency itself goes back to Latin flŭentĭa.

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

fluency
Of speech, linguae volubilitas or mobilitas; orationis celeritas; verborum expedita et profluens quodammodo celeritas: copia dicendi: expedita et perfacile currens oratio. Fluency in expression, facilitas (e.g., to acquire a perfect fluency in speaking, assequi firmam facilitatem, Quint., 10, 1, 59): that he may obtain greater fluency of speech, quo sit absolutius os (Quint., 1, 1, 37). [Vid: FLOW (of speech).]
Smoothness, levitas (as quality, also of expression).
Abundance, Vid.

Quick answer

What is the Latin word for fluency?
The usual Latin words for “fluency” are mōbilitās, levitās, facilitās. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.