Published in the late 60’s/early 70s and set on the coast somewhere in England, I think in Elizabethan times. The flying machine (a Leonardo da Vinci type invention) only works properly at the end of the book, when it is used to escape from some people of horseback – it flies over the cliffs and the children escape (maybe to France)
Changes trilogy (Weathermonger, Heartsease and Devil’s Children) by Peter Dickinson perhaps.