How did Nunnally and Sayoko survive the FLEIJA? The sheer action of the FLEIJA leaves behind a very neat crater and turns matter in its radius into a vacuum (airborne units tend to get blown into the blast center). How did Nunnally and Sayoko survive that?
This blogpost adequately explains how she could have survived.
I also do not believe there was as much of a vacuum because at that point in time the FLEIJAs still had a limiter. It was not until the destruction of the Capital city of Pendragon that the limiters were removed.
This is the summary of the link:

After Sayoko rescued Kallen she went on ahead to find Nunnally and to try and Rendevouz with Rolo and found the ship Nunally was on. Around the same time the Gefjun disturbers were disabled and Nunnally’s ship left with Sayoko and her men aboard.  She never passed Rolo because he hadn’t even reached the hangar yet.
Eight minutes later Rohmeyer is on a decoy ship with KF’s to make it look like the governor general is aboard and Rolo walks in to find the ship, assuming reasonably that Nunally is on it he commandeers a KF to try and blow up the ship and kill her.  Meanwhile Sayoko barges in on Nunnally in the ship she’s really on and Rohmeyer doesn’t respond at all because she’s actually on the decoy back in the hangar.  Nunnally’s ship is probably just outside the area by this point.  When the bomb goes off Rohmeyer is caught in it in her decoy ship and goes up in a ball of flames.  Rolo has run away once he thinks he knows what’s going on with Fleija (whatever it’s called) and somehow made it to safety.
How? I’m not sure as that thing had a pretty big blast radius.  So when he reports to Rolo he talks about the ship Rohmeyer is on and really isn’t lying when he says Nunnally is dead, because he honestly thinks she is.  In reality I think she’s okay and with Sayoko elsewhere.  Though that elsewhere might be in Schneizel’s clutches.