A B757-200 Captain experienced an engine flameout after start during push back.

Narrative

After pushback; we started the left engine. After what seemed to be a successful start; I decided I would start out single engine taxi using the left engine. I advanced the throttle to approximately 1.15 EPR when I realized the aircraft wasn't moving. I looked out my window to my left to confirm if the aircraft was moving at all. I noticed no movement. When I looked at the engine instruments; I saw that my EPR indication was around 1.13 EPR and there was no N1 or fuel flow indications. There was also a very strong smell of fuel fumes in the cockpit; followed by the Flight Attendant advising us in the cockpit of the same fuel fume smell throughout the cabin. We immediately shut the left engine down and pulled out the Quick Reference Checklist. We then contacted Dispatch and Maintenance advising them of our status. A conclusion was made that we had an engine failure. I asked Maintenance if they felt it was OK to attempt a restart. I started both engines with no problems and returned to the gate.