You have your light flashes; now you need to add the shooting-star or comet effect that coincides with each light flash. Each comet is made by animating a solid that's shaped by feathered masks:
Go to time 0;26, and create a white solid layer named White Line that's 200x50. The final line won't be nearly that large, but this size gives you room to feather the layer masks you'll add next.
Creating the first White Line solid layer
Use the Rectangular Mask tool (Q) to create a thin straight line within the solid. Be sure areas of the solid surround all four sides of the mask for feathering.
Press F on the keyboard to display the Mask Feather property in the Timeline, and set its value to 3, 3.
A feathered rectangular mask makes the comet trail
To add a small comet head, use the Elliptical Mask tool (Q) to draw an oval shape near the left end of the new line.
Set the oval mask's Mask Feather to 10, 10.
Adding a comet head by using the Elliptical Mask tool
Now you can animate the comet:
Turn on the lock next to each mask. Then, go to time to 1;01, where the first flash appears.
Line up the oval portion of the white line with the bright spot in the lens flare, and add a Position keyframe to the White Line layer.
Back up to time 0;26. To keep the line straight as it moves, hold down Shift while you move the White Line layer off the screen to the right.
To complete the cycle, go to time 1;06, and move the line off the screen to the left while pressing the Shift key.
The line should now zip across the screen, and the comet head should line up with the light flash. If you need to refine the size of the line, try changing only the y value of the solid layer's Scale property to thin the line and maintain its proportion relative to the feather.
You may have noticed that the Position velocity (the speed of the animation for the Position parameter) isn't even from start to finish. If you want to make the line travel at the same speed throughout the animation, expand the Position property in the Timeline, and deselect the box under the middle keyframe to make it a roving keyframe. Doing so makes the middle keyframe interpolate its speed from the previous and next keyframes.
Now that you've created one flying comet, you'll create duplicates of it and align the copies' timing with the other lens flares:
Select the Light Flash layer, and press U to reveal its keyframes.
Duplicate the White Line layer. Move the In point of the new White Line layer to time 1;16 so that it lines up with the start of the second set of the three Lens Flare keyframes.
Repeat step 2 three more times to create the remaining three lines, but align the In point of the new lines with the start of the other sets of Flare Brightness keyframes at times 2;06, 2;26, and 3;16.
Aligning the remaining lines
Press Home and then the spacebar to preview the animation. A comet should fly across the Comp window from right to left, and a flare should fade in and out to reveal each set of letters in the title.