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Multiple attack penalties mean that the rogue is very unlikely to roll all crits with four strikes in one round. An ancient gold dragon has an AC of 46 so even a pretty optimized rogue should have a decent chance of missing even with the first strike (20 for level + 6 for master proficiency + 7 for Dex bonus + 2 for flat-footed + 3 item bonus = +38).
The 2d10 persistent fire damage only applies at the end of the turn of the target being attacked and doesn't stack with itself (it's the same whether you critically hit once or four times). The 3d6 acid damage applies to the target's armor, not the target.
Ancient gold dragons, incidentally, are immune to fire.