That’s a good question—and one where you’ll get slightly different answers depending on who you ask.
For quality fluid steel 16ga and 20ga barrels, a commonly cited practical minimum in the forcing cone area itself is around .025"–.030", assuming the barrels are in good condition and free of significant pitting.
That said, many experienced smiths prefer to see more thickness than that right at the chamber/forcing cone junction, since it’s the highest-pressure area. General guidance suggests something closer to ~.080"–.090" at the end of the chamber/entry to the cone for a comfortable safety margin.
Bottom line:
.025"–.030" = often quoted minimum workable in the cone
More is better near the chamber end
Always measure carefully and consider barrel condition before any work
When in doubt, a competent double-gun smith’s opinion is worth it.