I read this article explaining flow around a fixed-sweep swept wing, and it stated that the spanwise flow component does not accelerate, but the chordwise flow component does. What is so special about spanwise flow that it does not accelerate?
In chordwise direction there is a curvature that accelerates the flow. In spanwise direction there is no such curvature. See this answer for a more elaborate description of the lift generation.
Notice in this illustration the line closest to the upper surface of the wing that depicts chordwise flow. Chordwise means the airflow is perpendicular to the wing whereby it encounters the airfoil shape. The curvature of the airfoil forces the air to change direction thereby accelerating it.
Spanwise airflow is parallel to the wing, and does not cross the curvature of the airfoil. This is like travelling along the side of a hill. Spanwise flow is not curved and therefore it is not accelerated.
Spanwise flow is associated most with swept wings or when yawing straight wings.
Whenever a mass is made to change direction, it is being accelerated: