The one time flash means that the Power Management Integrated Circuit (PMIC) saw something about your power that it did not like and went into self-protect.
The 5 V power for the BBB must remain between 4.5 and 5.5 Volts at all times. even a transition out of that range for a millisecond or so will trip the self protect.
There are also some rise-time requiremetns when the power is turned on.
It is best to stay between 4.75 and 5.25, so that you have some margin, against the self-protect points.
Put an oscilloscope on your 5V power and figure out what is happening.
--- Graham
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