G'day Fortunato,I think that, at 1776, the flageolet would have been relatively common, the recorder was going out of use in preference to the more powerful cross-blown flute, piccolo and fife but the flageolet seems to have survived as an amateur instrument right through. (The recorder was revived in the early 1900s.)
The tin whistle is a product of the industrial age and probably did not exist in any form in 1776, although its immediate ancestors, simple six tone-hole whistles of wood, were common and are in an unbroken line back, at least, to neolithic whistles of wood, bone and reed.
The flageolet seems to have still been around in the Victorian age as the "Shepherd's Flute" (probably a fanciful name) because of the soft intonation that came from its bulbous air chamber above the fipple 'balancing out' the air pressure and producing a quiet flowing melody, so it may well have been very appropriate for a young man to play to his love.
Regards,
Bob Bolton