Q: If Garchomp C LV.X uses Dragon Rush and discards DCE is Scizor Prime damaged?
A: No it isn't.
More info on Scizor Prime:
If something is considered a 'cost for an attack', it would include wording such as 'in order to use this attack'. Otherwise it is an attack effect, and therefore done after damage.* Therefore the Flareon bit makes sense.
However in regards to Dragon Rush, it doesn't get damaged either. The reason for this is because the discarding of energy and the doing of damage are considered to happen at the same time. Why is it like that? Japanese wording. Leave it to them to screw everything up. Chrisbo did say I had a very valid point as I did go with the English wording (discard, then choose, then damage), but because of the Japanese wording, Dragon Rush won't work either.