For a pair of complete and utter low budget howlers, one needs look no further than
a) the episode
"Private Plane" of Blackadder Goes Forth where they become pilots, and end up flying something suspiciusly tigher-moth like, presumably dressed up to look like an SE5. The clincher is when they are shot down by the German single seater wich has a fairly obvious canvas cover over the passenger cockpit...
b) The second equally low-rent production would be that crime against aviation culture known as
Biggles Adventures in Time, featuring a distincly 1930s biplane in 1917, and a world war one pilot who can fly a helicopter...