I’d try just making a couple solids. One red, and one white (or whatever colours you want really). Mask out the shapes you want to reveal (probably with rectangular mask), then either…
A) Set each solid’s anchor point to the leftmost side of its mask, and as Ben suggested, adjust the transform properties (probably scale horizontally) and keyframe them to a timing of your liking.
OR
B) Animated each mask’s path so that it goes from thin to wide.
OR
C) Apply a Linear Wipe effect on each solid, and animate from beginning to end accordingly.
The advantage to “A” will be that you will be able to achieve a motion blur, if that is what you want. As for the rest, the font looks pretty familiar, maybe trebuchet?
Design is what you leave out.