Looking for the base part of a flag mirror.

For "stuck" screws the usual suspects will make their appearances... Heat, soaking with PBlaster or a 50/50 mix of acetone and ATF (this stuff stinks).

You can drill it out at the risk of destroying the threads, but as the base is likely pot metal you could try filling it with solder, re-drilling and tapping the hole.

Or if you can find a slightly larger setscrew and tap (neither need be metric), you can use it in a larger threaded hole.
 
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