@Edward Clarke Sopwith Camel Biplane Fighter (1917)
Excellent idea (even if it does remind me of an old Fry & Laurie sketch, "What is the name of this camel who lives with you in Greenford?..." - does anyone else remember that or is it just something dark, vivid and unpleasant from my imagination?).
For my money though, the best aircraft for the Red Arrows would be the Bede BD-5, as seen in Octopussy. Although getting a display flight aloft in one would be difficult, given the colossal, heavy steel balls that would be needed to fly several of them in close formation...
Icon shows the probable resut of attempting to fly the Bede BD-5.