Copyright infringement can get complex but this is one of the simple cases. Was the software under protection? Yes. Did the redistributor have permission? No.
The .NET file that Adobe served a DMCA512 notice on doesn't contain any of Adobe's copyrighted code. It's an unpacker and installer that users run on the software they download separately from Adobe's Chinese distributor.
This is emphatically not a copyright violation of ANY kind, but it's especially not a violation of copyright that would entitle Adobe to use DMCA 512 to have it expeditiously removed. A DMCA 512 claim is explicitly - and solely - a mechanism for removing unauthorized copies of a copyrighted work. Again, this is a .NET file that has instructions for unpacking a standards-defined .ZIP archive and then installing its components. It's NOT a copy of Adobe's code. DMCA 512 has no place here.
And while it's NOT a violation of DMCA 512 to host this batch file, it IS a violation of DMCA 512 to file a baseless takedown against it. The DMCA's requirement for a "good faith belief" that a file infringes copyright, "on pain of perjury," makes Adobe the sole lawbreaker in this story.
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Separately: You might be wondering if this is a DMCA 1201 violation (that's the part of the DMCA that deals with "circumvention" of "a technological protection measure" that "controls access" to a copyrighted work.
It's not. There's no TPM in a ZIP file, so there's no circumvention in unpacking it.
But even if it was, Adobe didn't send a 1201 takedown (those don't really exist, because there's no 1201 safe harbor, though sometimes firms send 1201-related cease-and-desists), they sent a 512 takedown.
Again, a 512 takedown only ever applies when there is distribution without authorization. There is no distribution. It's inarguable - and provable. The .NET code is (was) on github for anyone to inspect. It is unequivocally NOT a copy of Adobe Flash or any other work that originated with Adobe.
Unrelated, are you the DoctorOW who sent me a password reset link today?
BTW, it looks like at least one version of the installer included a binary, though the creator says that's not true anymore, so you were (partially) right and I was (partially) wrong.
P.S. If the CleanFlash installer contains the Flash Player distribution, instead of downloading and patching it on the user's machine, then the author indeed deserves to be slapped with a complaint for such an obvious blunder.