In Nick's design,each segment is lit full on with up to the limit of the segment (typically 20mA) for 1/28 of the cycle time.
If you want it flicker free, you want to cycle thru all of the segments 24 times/second.
So, drive-time for any segment is 1/24 second/28 segments = 1488 microseconds.
So you can write your loop to check when 1488uS passed, when it has turn off the current segment and turn on the next segment. That's single segment multiplexing.
Check the spec on your display - individual LEDs are often spec'ed for a higher current for short periods - if your display supports that you drive like 35mA vs 20mA to make things look brighter.