The major difference in a flash "Run Cycle" is that both feet must come off the ground sometimes. Thre is still a left cycle and a right cycle. You can still repeat the first 3 frames and get a full cycle just like the walk cycle lesson. However it's best to make every frame look a little different because of the speed of the "run cycle" itself. You should make your run cycle at least 6 frames and slightly alter the position of similar frames (frames 1-4,2-5 ,3-6) or human eye will recognize the 3 frame pattern which is bad because it gives you a flicker look.

Spend the time and do the run right. Trust me!!!

Let's break it down.
keep in mind the 3 frames Right, 3 frames Left still applies.
The left cycle is in a tinted NAVY, the right cycle is in BLACK

The Breakdown:

Frame 1 BLINKY IS TOTALLY OFF THE GROUND!!!!

Right foot off the ground and in the full back position. Left foot off the ground and moving forward position Right hand is in a fist and moving forward. Left hand is in a fist and moving backward.

Frame 2
Right foot is still off the ground and moving forward. Left foot is fully extended forward striking the ground.
Right arm is full forward, Left arm is full back.

Frame 3

Right foot is passing center moving forward. Left foot is on the ground at full contact in the center.
Left arm is moving forwards, Right arm is moving forward.

Frame 4 BLINKY IS TOTALLY OFF THE GROUND!!!!

Left foot off the ground and in the full back position. Right foot off the ground and moving to forward position. Left hand is in a fist and moving forward. Right hand is in a fist and moving backward.

Frame 5
Left foot is still off the ground and moving forward. Right foot is fully extended forward striking the ground.
Left arm is full forward, Right arm is full back.

Frame 6
Left foot is passing center moving forward. Right foot is on the ground at full contact in the center.
Right arm is moving forward, Left arm is moving back forward.