The fourth Kill la Kill drama CD (bundled with the eighth BD volume) narrates how everyone escapes Honnouji Academy after Satsuki blows the place up. It is truly a riveting tale of discomilfery and nudity.
In short: the Divine Generals split into two groups in order to lead the people of Honnouji away from the COVERS, which are in hot pursuit. Sanageyama and Nonon lead one group away by helicopter, while Inumuta and Gamagoori lead the other group away by truck. They plan to rendezvous at Rinne-do Middle (i.e. where Satsuki and Gamagoori went to middle school).
Sanageyama and Nonon's group proceed by helicopter - but as they approach Rinne-do, they see that it has already been overrun by a group of COVERS. Nonon goes forth in her Symphony Regalia (which can fly, keep in mind) to dispatch the COVERS. Before long, her uniform experiences too much strain, resulting in its nexus thread snapping. She falls out of the sky, whereupon Sanageyama activates his Sword Regalia to go forth and save her - but it so happens that Iori and Soroi arrive just in time on another helicopter to catch her. Iori then deploys some sort of instant-freeze weapon to dispatch the COVERS. They decide to rendezvous with the truck convoy ASAP.
Upon hearing from Sanageyama that Rinne-do had been overrun, Inumuta and Gamagoori decide to divert to the Nudist Beach base in Osaka (under advice from Mikisugi, who has Ryuuko and Senketsu in tow and is following them in his DTR - yet another amusing incident) and have the helicopter group do the same.
To protect their convoy, Inumuta and Gamagoori hatch a plan. While Inumuta extends his Probe Regalia's active-camouflage feature over the entire convoy to conceal it from the COVERS, Gamagoori waits behind with his Shackle/Scourge Regalia to destroy the COVERS that are in pursuit, to ensure that they cannot destroy the bridge connecting Honnouji to the mainland and sink the convoy as it crosses. They both succeed; alas, the strain on their uniforms is too strong, and both of their nexus threads snap. Tsumugu happens by and picks up Gamagoori (who is in the nude, having lost his uniform, and thus of course earns Tsumugu's trust) on his way to join up with the convoy.
After that, both groups successfully arrive at the Nudist Beach base in Osaka, and the rest is history. Sanageyama's uniform was saved from terminal damage at the hands of the COVERS by Iori's timely intervention; the other three were not so lucky.
In long: you should definitely listen to the drama CD. Even if you don't know Japanese, it's worth it, if only to hear more of Gamagoori and Mikisugi yelling.