I'm not aware of a different symbol used just because a relay has a flag on it or not, the flag is a visual indicator for when someone is physically looking at the relay, it makes no difference in the operation and I can't see a purpose for having a special symbol for it in a diagram. I've never run across that either.
That symbol, as mentioned above, is much closer to looking like a JIC Flow Switch contact, although usually they are not shown as Double Break like that. IEEE 23 is a temperature relay function, but the JIC wiring diagram symbol for that is different.
Common JIC standard wiring diagram symbols