First, the boring-but-real part. Your chocoflan has eggs. And milk. So, temperature danger zone, people.
Leaving it out all day is a gamble. A risky, bacteria-filled gamble. Your stomach is not a casino you want to play at.
The official answer? Yes, refrigerate it. After two hours at room temp, things get dicey. Your flan layer is basically a custard, and custards love the cold.