I can tell you one of the text books that I have on fluid dynamics for yacht
and ship design (I design racing yachts and do composite construction and
analysis) has a lot to say about flutter and avoiding it in water. Since the
Reynolds numbers can be very close I would assume that the same would hold
true of aircraft.  Perhaps someone has data about what happens in air to
either validate or show that the two are not comparable.

One of the problems with flutter analysis that I've seen for aircraft (and I
took Martin's aircraft design class) is that it is done devoid of any
aerodynamic input which can have a huge impact on the dynamics of the system,
at least in water.  In water testing, (a medium 300x denser than air but at
similar Reynolds numbers) a movable control surface, say a rudder trailing a
stabilizer that is slightly fatter than a fair line from the stabilizer is
resistant to flutter.  One that is exactly fair with the lines of the
stabilizer is also resistant but not to the degree of the first one.  A
rudder that is slimmer than the fair lines of a stabilizer is prone to
flutter.  This is due to the control surface flying in the wake turbulence of
the stabilizer.  It also has to do with the stiffness (modulus) of the whole
system and having the dynamic excitation of the system coincide with the
natural harmonic frequency of the structure.  Once beyond that critical
speed, the vibration will stop again (if you have any control surfaces left).

Anyone have any experience or data on foils in air?

Dan Newland
Super ES