Some doubt that this is a J.S. Bach composition, but it's likely that it was composed by a Bach, as one music site puts it:
No copy of this sonata has survived in Bach's hand, yet that's true of all but one of Bach's flute sonatas. Some musicologists suggest that this is the work, at least in part, of C.P.E. Bach or some other composer, yet the authorship has not been disputed seriously enough for this light, entertaining piece to be banned from the Bach catalog. Here, the composer takes note of the emerging galant style of the 1730s, with light textures, simple harmonies, and highly ornamented melodies. The sonata falls into three movements, the pattern familiar from Vivaldi concertos rather than from the more sober, four-movement church and chamber sonatas of the immediately preceding decades. (Bach continued to employ this latter style in several of his other sonatas from this same period.)It’s a delightful piece, full of light and air; and, moreover it has the hope and optimism so uncharacteristic of the period in which we now reside.