Violoncello 1 was Gunn's first publication, but the first record of Gunn as an instrumental performer is as a flautist. He wrote two books about the flute: The Art of Playing the German-Flute, and its sequel, The School of the German-Flute. The date of publication of Flute (Art) has often been given with some qualification, but Reuss's catalogue states 1793, and it was reviewed twice in that year. Flute (School) was published as ‘Book the First’ but there was no second part. The introduction to Flute (School) clearly refers back to the earlier work which suggests a publication date not too long after Flute (Art), often plausibly estimated at 1794–5. However, this is not clear. The title page gives Gunn's Bennet Street address, and lists his other publications as Flute (Art) and Violoncello 1, so it would appear to have been published – or at least engraved – before the publication of Violoncello 2 in 1800. But no newspaper or periodical advertises Flute (School) in 1794 or 1795. There are copies of both flute works in the British Library, each with a watermark for 1807 which could indicate a second issue of both works at the same time. But the first advertisements for Flute (School) do not appear until as late as 1812. After returning to London in that year, Gunn reasserted his presence there by ‘marshalling’ his publications on the cello and the flute. Flute (School) was then advertised as a new publication:

To summarise: the title page of Flute (School) and its relationship with Flute (Art) support a pre-1800 date of publication (in which case there was a later issue printed on paper dated 1807), and this is supported by the title page of Essay (Harmony) (1802) which lists both works.