A321 Captain reported an engine fire had developed when they were starting a second engine while taxiing out for takeoff. Engine was shut down and they taxied back to the gate for maintenance.

Narrative

We single engine taxied out on engine 1 with the APU running. Approaching the departure runway I called for the second engine to be started. During the second engine start we got an Engine 1 bleed not closed ecam. We turned the bleed off per the ecam. Number 2 started. We then received and ENG1 fail ecam with rollback. The EGT kept climbing. I told Tower we would need to stay in position while we ran a checklist; and then when ATC inquired if we needed assistance; I asked for them to bring out the trucks. We briefly debated running the engine fire on the ground QRC; but then decided to run the engine tail fire qrc which the FO ran. Aircraft behind us confirmed there was fire coming out of the back of the engine. I called cabin crew for them to assess. I made a pa after the temp was decreasing but before the trucks got there so the customers wouldn't be alarmed. Dry motoring put out the fire. The FO called Ops and arranged a gate for us to taxi to. ARFF (Airport Rescue and Firefighting) confirmed there was no fire and we taxied to the gate with them following behind. Another PA was made before we taxied to the gate. A Logbook entry was completed.