for synchronize- no, because status clause. telepathy has previously been answered 2 posts above to fit under damage clause because it blocks any attack aimed at an ally even in doubles. flash fire and fluffy already dont grant the mentioned moves. same goes for the immunity abilities you mentioned. eerie impulse triggers lightningrod so it is granted by it, while magnet rise is not. did you check the link with the movelists? its all there.An interesting idea, but it needs some refining. For example, shouldn't Pokémon with Synchronize get moves that cause status afflictions relavent to the ability, like Thunderwave, Poison Powder, and Fire Blast?
It also seems like Telepathy should get Ally-affective moves like Explosion and Earthquake, although that may be arguable for a singles format. It should certainly be allowed if this ever goes into doubles.
Abilities like Flash Fire and Fluffy interact with offensive fire-type attacks, but not every fire-type attack qualifies. Sunny Day, for example, doesn't activate Flash Fire. The same can be said of Dry Skin, Volt Absorb, Water Absorb, Lightning Rod, and Storm Drain (Magnet Rise, Eerie Impulse, Rain Dance, Withdraw).
You should probably tie banned abilities to the clause that they fall under, as well. Aerialate, Liquid Voice, and Normalize are allowed, for example, while Pixilate, Galvanize, and Refridgerate are banned. Normalize would allow Delcatty access to every offensive move, at least, and it should probably fall under the Umbrella Clause. I didn't see the clause that caused the differentiation in the other abilities - or even one that would cause Pixilate, Galvanize, and Refridgerate to be banned, however.
normalize already falls under umbrella clause. aerialate was unbanned because it doesnt get given to any base form mons, so nothing can take advantage of it. liquid voice is unrelated to those moves, and only grants sound moves. that being said, its also unreleased.
http://pastebin.com/J0ADe4Sf
edit: regarding synchronize i see what you mean in that it only transmits 3 status conditions. will look into this to see if its banworthy, otherwise will implement