Normally we would simply say
The children walk to school.
The phrase on foot is typically used to draw attention to the fact that some other mode of locomotion was not used or could not be used:
We drove into the jungle in our 4x4 vehicles, but we had to abandon
them and proceed on foot when the dirt road ended. The vegetation was
It is possible that your context could support the use. For example:
The school bus gathers children from the surrounding villages and
brings them to the school parking lot. But the school is perched high up on a
hill, overlooking the valley, and the children must go the final quarter mile on foot.