You only see the brief flash when applying power or when the IDE uploads the code and hard resets via RTS.

If you do this:

#include <M5StickCPlus.h>
void setup() {
M5.begin();
digitalWrite (M5_LED, HIGH); // turn off the LED
pinMode(M5_LED, OUTPUT);
digitalWrite (M5_LED, HIGH); // off
}
void loop() {
delay(10);
ESP.restart();
}

the LED does not flash repeatedly.

I don't see the brief blink myself, but have you tried to swap the two statements?

Thanks
Felix

Bear in mind that when you initialize the pin with:

M5.begin();
...
pinMode(M5_LED, OUTPUT);
digitalWrite (M5_LED, HIGH); // turn off the LED

The LED will blink briefly. I don't know of a workaround. I also know virtually nothing about ESP pin frobbing.

One pin of the LED gets wired to +V and the other pin goes to the GPIO.
At some point there is most likely a resister to limit the current.

Apparently its easier (less heat?) for the GPIO (pin) to source power by pulling the circut "low".