They have not been clocked but certainly some fast-flying skippers can fly 30 mile per hour or faster. Slow flying butterflies probably fly 5 mph or a little more.
During fall migration migrating Monarchs have been seen flying by tall buildings such as the Empire State Building at 1,000+ ft. Butterflies are picked up by storm fronts and moved 100's of miles, probably at altitudes of several thousand feet.

