There is no autothrottle self-test, at least not one that manifests itself in the flightdeck.
What you are seeing is the usual A/T flashing amber meaning airspeed error. This is only active inflight when the flaps are not up and the actual speed is not within +10 or -5kts from commanded. You will see this every times you select flap 1 (from flap up) because you will also presumably select the speed associated with flap 1 which be about 20kts less than you present clean speed, hence more than 10kts over bug speed.
If you want to prove this, preferably in a sim, from clean speed select flap 1 it will not flash, now select the flap 1 speed and it will flash until your speed falls to within 10kts of it.
It is all in your FCOM.
S&L