This recipe says to cook in loaf pan, putting caramelly mix in pan 1st, then eggy mixture.
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Trust the process, if you've followed the recipe from ATK, it should be fine, the caramel should release when you unmold it. If you feel like it is sticking, you could steam the bottom of the mold and try again. Deep breaths, you're probably fine.
I understand your concern, but it actually doesn't matter if the caramel doesn't all come out when you flip the flan, as long as the flan itself slides out complete. Any remaining caramel can get loosened and poured over the flan . The technique to loosen it is the same, either way. Put the loaf pan back into its larger 'bain marie' pan(that has been emptied of its original water) with enough boiling water in it to heat up the bottom of the flan pan.Let the flan pan sit in there for ~ 5-10 minutes until, when you tilt the flan back and forth, you see the liquified caramel around it.
An update on the flan:
Trust the process. Great advice! And when I slipped my knife around the pan before the flip, I did see some caramel sauce peeking around the edges of the loosened flan, as both of you noted. It came out of the pan beautifully!! I will make this again!