Blood flow is non-uniform due to varying nature of blood pressure during heart beat cycle.
Blood flows from heart to various parts of our body through Arteries. Various blood carrying vessels are : arteries, Arterioles, capillaries, veins.
The blood pressure in the arteries just outside heart is maximum just when blood is pumped out. Then it reduces to diastolic pressure value and then increases back to systolic pressure at the next heart beat. This pulsating nature of blood flow, that is a certain volume of blood is pushed out of heart periodically, is the reason for the non-uniform flow.
When pressure is high at a point in a blood vessel, the speed of blood flow is high. When pressure is low, then speed is low. Also, the blood vessels are flexible expand differently for different pressures of blood flowing through them.
Further the gravity due to Earth acts on the blood. Hence, the blood is also accelerated / decelerated due to acceleration due to gravity g.
Thus the speed of blood flow varies in time and according to size of the blood vessel as well as the time from the closure of aortic valve in the heart.