To get more brightness, spend more time with the LEDs on:
const unsigned long delayWhileLit = 1; // Increase this until you get flickering, then reduce a step
void writeMinutes(){
PORTD = segBytes[minLeft]; // display left digit
digitalWrite(leftMinAnode, ON);
delay(delayWhileLit);
digitalWrite(leftMinAnode, OFF);
PORTD = segBytes[minRight]; // display right digit
digitalWrite(rightMinAnode, ON);
delay(delayWhileLit);
digitalWrite(leftMinAnode, OFF);
}
void writeSeconds(){
PORTD = segBytes[secLeft]; // display left digit
digitalWrite(leftSecAnode, ON);
delay(delayWhileLit);
digitalWrite(leftSecAnode, OFF);
PORTD = segBytes[secRight]; // display right digit
digitalWrite(rightSecAnode, ON);
delay(delayWhileLit);
digitalWrite(rightSecAnode, OFF);
}