I think that most if not all ships should be able to temporarily go to flank speed at a loss of weapons and shields.
The whole notion of flank speed is that after a certain point (a ship's rated speed) a ship can continue to speed up, but the amount of energy it consumes will multiply much faster than the gain in speed (ie it is very inefficient).
As such, a ship could hypothetically move at two to three times its rated speed until its power reserves run dry and it is back to generator only.