When you attempt to sweetspot after SDI'ing out, sometimes the Charizard will not stop the Flamethrower and you might get swamped by it again. If that happens, SDI back out again and keep trying until the attack becomes small enough for you to sweetspot the edge or straight up blast through it. If you constantly SDI out of it quickly you will not eat too much damage.
Be extraordinarily careful when setting up that sweetspot though, cuz if it isn't absolutely perfect Zard can meteor you with Dsmash(assuming he or she turned off Flamethrower with the proper timing). Although if you do that thing where you drift out from the ledge a bit while UpBing and then grab it, Zard Dsmash will whiff, so give that a shot.
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One other thing, if you're really good at it, you can attempt to SDI back onto the stage. You cannot get past Charizard while he's Flamethrowering, but you can get to the ground in front of him and crouch cancel shine. This maneuver will hit Zard and clank with Flamethrower so you can't necessarily get a follow-up, but hey you ended the edgeguard scenario, so that's cool.
Be careful about Charizard turning off Flamethrower while you're trying this one because if you're still offstage when this happens you may accidentally kill yourself if you're not paying attention.