The earliest US patent on the topic is thought to be Delaware doctor Watson Fell Quinby who in 1867 patented his Flying apparatus, illustrated below.
Quinby proceeded to patent variations on the concept, with, in 1869, his Flying machine, illustrated below...
Fluttering wing aerial propelled apparatus suitable for carrying a man, illustrated below. The inventor was Alfred Ernst, writing from an Italian address.
Human powered flying garment. It has an interesting description, stating that it is made to resemble a bat and has a wingspan of 13 feet, "made to measure its inventor". Despite this hint, I do not know if it's actually been tried out (the same goes for the previous patents). Helium-filled balloons are included to aid lift. Below is its main drawing.
Six patent specifications were listed by the patent examiner as being of some similarity.
So, is this old dream impossible ? Not so. In 1979 the English Channel was flown using muscle power alone, in the Gossamer Albatross, which won it the 2nd Kremer Prize for human-powered flight. An amateur cyclist managed it, flying at a top speed of 29 km per hour at a height of 1.5 metres above the waves. Taking off from the cliffs on the British side did help, but he still took 2 hours and 46 minutes. A patent for the aircraft was published as Lightweight aircraft by Dr Paul MacCready and others. The main drawing is given below.
This was a successor to his Gossamer Condor, which had already won the 1st Kremer Prize -- and was flown by the same intrepid cyclist, Bryan Allen. New and light man-made materials as well as clever design were essential.
Below is a video about the English Channel crossing of the Gossamer Albatross.