The Proof 1857 Flying Eagle Cent is tied with the 1858 Large Letters as the scarcest Proof date of the type. Yes, that is correct, the Proof 1857 "Flyer" is scarcer (actually much more rare) than the vaunted 1856. A look at the current (October 2011) PCGS Population Report confirms that PCGS has certified 725 Proof 1856 Flying Eagle Cents, but only 59 of the 1857. That is less than one tenth of the population of the 1856, yet it sellls for a much lopwer price. This illustrates that publicity often trumps actual rarity in the coin market, and it may mean that the 1857 has excellent price growth potential.
The majority of the Proof 1857 Flying Eagle Cents certified by PCGS are brilliant, with little or no cameo contrast. However, the Cameo designation is a fairly recent phenomenon and there are doubtless some coins among the "brilliants" that would meet the Cameo criteria if they were resubmitted today. Nonetheless, Cameo Proof 1857 Flying Eagle Cents are very scarce. To date, no Deep Cameo Proofs have been certified by PCGS.