Does Espeon's "Solar Revelation" Ability prevent the flipping of coins for an attack that does damage times the number of heads flipped?
No, it does not. Flipping coins in this context is used to calculate how much damage is to be done. Since "doing damage" is not prevented, the flipping is not prevented either.
Source: TPCi Rules Team (2012-05-10)

Relevant cards

Note: All applicable cards may not be listed below.
BW5_48
BWP_BW92
BWP_BW92