Nifft,
In two years of AE, I have yet to see a PC Greenbond who didn't multiclass, so if you want to go straight through for 20-25 levels, more power to you. I've just noted that the grab for armor and weapon proficiencies (and even skills or combat rites) has been very tempting for my local group, and figured I'd toss it out as a suggestion. Mystic Secrets, Transcendence, and the Spell Treasury supplements for AE also have a lot of nice things for Greenbonds.
As for the Dracha...
1) Diplomacy as a permanent class skill is a nice house rule, although in the case of spellcasters, I might let them choose one benefit or the other so as not to imbalance it.
2) My suggestion is to limit your multiclassing unless you think the game won't survive beyond 10th level. Both Akashic x/ Dracha 6 and Champ of Knowledge x/Dracha 6 will be solid multiclassed builds. Adding a third class could cripple the Champion of Knowledge build entirely, whereas the Akashic build might gain benefit from multiclassing with Totem Warrior, Unfettered, or Warmain. Your key ability scores are going to be Int and Con. I reccommend a High Con Akashic build, and a High Int Champion build, since either one will yield you serviceable HP and decent skills (remember, C.o.K's get 4 +int skillpoints unlike other champions). Since you're a Dracha, don't worry about Climb, Jump, and Ride ranks, since you'll have a good Strength and eventually flight, which will make those superfluous. If you're DM is allowing that Born Leader variant, then you should just focus on keeping Diplomacy maxed out, and not worry about Bluff, since Dracha are, by the book, a little straightforward and naive, unused to concealing anything about themselves.
By way of RP advice, I'd say that both builds lend themselves to the idea of a Draconic Philosopher, a Scholar/Paragon, very much proud of his origins, and seeking to increase his understanding of what it means to be a Dragon. His taking racial and evolved levels is just an extension of this desire to be as Dragon-like as possible, to blur the line between himself and his creators/masters. While diplomatic, he should make it quite clear that he believes the Dragons to be rightful masters of Terakal, and that the Giants have broken the ancient treaty. Or perhaps, he has doubts about the treaty, which in turn makes him eager to seek proof of his master's claims, secretly afraid that perhaps the Giants might be right, and what affect that will have on all of Dragonkind (Dracha and Dragon alike). Maybe he's an advanced scout or researcher for a Draconic Master, sent out to investigate matters of Draconic importance (i.e. proving that such-and-such area was once part of his line's territory, and thus should be returned to him as his birthright/prior claim). Whatever the reason, he should be confident, intelligent, and powerful, while having some quirk of his Dracha mentality that holds him back from being the Great Leader he's supposed to be.
Robert "The Other Guys Are Throwing Out Some Good Ideas Too" Ranting