If I have a single Rainbow Energy attached to Moltres & Zapdos & Articuno GX, can I use the extra effect of its "Sky Legends GX" attack?
No, even though Rainbow Energy provides all energy types simultaneously, it only provides one unit of energy. You can use it for either the Fire or the Water or the Lightning, but you still need additional units of energy for the other required types.
Source: TPCi Rules Team (2019-11-14)