As a general rule, the determining factors in deciding if the engine has suffered a "simple" flame-out, or damage which would preclude a re-start attempt are -
(1) Fire (as you've mentioned),
(2) Loss of Oil Pressure preceding the failure,
(3) Excessive EGT preceding the failure,
(4) Excessive vibration unassociated with compressor stall preceding the failure,
(5) Foreign body ingestion,
(6) Engine overspeed.
All of the above are good indicators that the engine has failed due to or associated with damage.
Regards,
Old Smokey