So, you want to know why velocity and pressure in fluids don't go hand in hand. In other words, you want to know why veins do not have high velocity = high pressure or low pressure= low velocity?

A layman's (non-professional) answer could be that veins experience x amount of pressure and the body relieves the excess of x amount of pressure by increasing flow (velocity) of blood. An exchange, if you will, in order to create a system of balance in your body.

Let's discuss some real-world examples.
Liquid: You have to pee really bad, that feeling that causes you to squirm, your face to turn red, and your chest to hurt is due to the high pressure exerted on the bladder wall from the encased urine (the liquid which is experiencing low/no velocity). As soon as your bladder (the thing that holds urine) begins to evacuate (the urine or fluid moves at high velocity), you can feel the pressure begin to decrease (the bladder wall begins to feel a low/no pressure) to the point you feel relief. Simply put, this happened because the urine vacated or left the body with velocity; thereby, lowering the pressure which in turn relieved the discomfort the person was feeling.

Gas: you breathe in very deeply; you feel your lungs fill with air. You feel like your lungs are full and you know this is true because you cannot breathe any more air (the gas which is experiencing low/no velocity) into your lungs. That feeling of fullness is the high pressure being felt on the lung walls. You then exhale, as you exhale (the air or fluid moves at a high velocity) you notice that there is less fullness or low/no pressure in your lungs. Simply put, this relief or lowering of pressure happened because the air vacated the body with velocity. Try it and experiment with in taking air slowly and quickly; thereby, changing the fluid's velocity, pay attention to how your lungs feel or perceive pressure as you breathe in and out.

To this end, have you noticed that when you exercise, that your blood pressure increases then it will level out even though your body is at work? That is because your blood will flow at an increased rate (velocity) to lower the pressure on the vein walls and will do so just enough to keep the system going at the pace of work, it is undertaking.

It operates as a self-regulating system of balance and it is only achieved with a low to high or high to low exchange. In fluid physics, most systems try to find a natural balance between the object such as the bladder, lungs hose, balloon, container, tube, etc. (non-fluid) and the fluid such as urine, air, oil, water, helium, milk, etc. (liquid or gas).

Why do veins have higher velocity compared to capillaries?

Now you may be wondering, why blood in veins has a higher velocity as compared to capillaries.
That answer comes down to the work of the veins in comparison to the work of the capillaries. When I say work, it is a type of force. Remember, force is the push or pull applied on an object. When force is applied to or on an object and the object moves as a result then we say "work" has been accomplished. Another way to look at "work" is it is an outcome or result of an action.

What is Bernoulli’s Principle in relation to blood pressure and velocity?

Daniel Bernoulli, a medical student, discovered that fluids (have no shape and yields to external pressure such as a liquid or gas) with high pressure will have low velocity and conversely low-pressure fluids will have high velocity. Amazingly, he was studying blood pressure in relation to circulation. What he found in his experiments using constricted tubes was high pressure=low velocity and low pressure=high velocity. You may also be wondering if the size of a "container" or "tube" is relevant, it's not; but, the shape and compressibility of the container or tube will have baring. It's interesting to note that having more of something (liquid/gas) doesn’t cause higher or lower pressure.

What about Pascal’s Law in relation to blood pressure and velocity?

Regarding fluids, are we saying, if it has velocity, it is moving fast?

The range of velocity and pressure can vary widely. Using the previous example; you can breathe out very, very slowly and although the velocity of the air exceeds the pressure, it may not be by much; but the velocity is still higher than the pressure. The other example, while holding your pee, you begin leaking urine slowly, momentarily the velocity began exceeding the pressure until you force your muscles to stop. As pressure builds, the urgency will continue until the leaking occurs again. In both cases, the velocity, only just, exceeded the pressure.

Simply put, the movement of these fluids through velocity is the body's only way of relieving or lowering the pressure in the organs, it doesn't necessarily mean it happens fast or quickly. I hope this helps answer the initial and related questions concerning force, pressure, blood flow and velocity.