No annotations needed for Final Crisis #7 from the Legion perspective. We get a couple of panels of Starman and a page or two of the new Miracle Machine (which, honestly, looks steampunk of all things).
But FC#7 also showed the irrelevance of "Legion of Three Worlds" to the Final Crisis storyline. It's not even complete yet, while the main story is over. Was the whole purpose of L3W to get the Miracle Machine to Superman? Here's Grant Morrison at Newsarama with the intended reading order:
NRAMA: Speaking of Superman Beyond – how does the timeline work between Beyond, Final Crisis and Legion of 3 Worlds?
GM: The Monitrix Zillo Valla recruits Superman’s help in Final Crisis #3 which leads into Superman Beyond #1 and 2, both of which happen in the space between Lois’ final heartbeats. He returns to save her in Beyond #2, only to be contacted by the Legion of Super-Heroes to deal with an emergency in the 31st Century – as seen in Legion of 3 Worlds #1. Normally, the Legion is able to return him to his own time an instant after he left, so naturally he feels secure quitting Earth after saving Lois. After his encounter with Superboy Prime in LO3W, however, he returns late to Final Crisis #6, to find time has crashed, Darkseid rules the world and Batman is dead. Oops.
Fortunately, he brings with him the means to save us all.
Over at Tim Callahan's "When Worlds Collide" at CBR, he fits the Legion into the whole Final Crisis story thusly:
Everything written by Morrison matters, and everything written by everyone else does not (with the possible exception of "Legion of 3 Worlds," but while that series may turn out to be an excellent addition to your library of awesome comics, it seems that all you really need to know about Superman's adventures in the 31st century is that he was indeed sent there during the middle of "Final Crisis" -- which conveniently removes him from the action, a point I'll discuss below -- and that Brainiac 5 showed him the Miracle Machine before sending him back, but that scene is included in "Final Crisis" #6 anyway)...
...And Morrison emphasized the centrality of Superman not just by showing his multiversal doppelgangers, but by removing him from "Final Crisis" during the middle of the series. The world fell into darkness so quickly -- the anti-life spawned so many Justifiers -- because Superman was not around. Batman was captured, Wonder Woman tainted, and Superman absent. But it was Superman who mattered most. The first DC superhero. The symbol of hope. The sun god. The light in the darkness.
Thus, L3W is a Final Crisis crossover because it explains where Superman is and why he's there during Final Crisis, not because it has great relevance directly to the story other than the Miracle Machine. (Though how can you return late from the future, no matter how long the L3W battle takes?)
So it's nearly certain that we'll see Bart Allen come out of the lightning rod. And Johns has said that the events of this miniseries (whenever the last three issues come out - come on, we had one in August and one in October, with one more in February; what is this, a quarterly book?) will ripple through his other books, which I guess mean Flash and GL.