I have a Beckett AFG burner with a Beckett R7184A Interrupted Ignition Oil Primary Control. The fuel line filter was clogged so I replaced it with a new one. When I turned power back on the burner tried to ignite but after 10 seconds or so it shut down. Now the burner will not start and the green light flashes (1/2 second on) which according to the R7184A dianostic table this means it is in lockout. I press the red button but nothing happens.

Shut off all power. Wait then turn back on. Did you bleed the pump?

I attempted the process of bleeding. Not sure if I got all of the air out but the burner did fire up and run for approximately 5 minutes then all of a sudden you could hear the flame kicking in and out and then finally out...

Sound like you still have air getting in the line or the filter housing/flare nut connections are leaking allowing air to get into the system. I am sure you have checked to make sure you have oil?