How does Viagra increase blood flow to that part of the body specifically, and not other body areas?

It doesn't it is a PDE5 inhibitor. That mechanism will increase blood flow wherever it is in the body, just happens to be in the penis but also in other places. Most notably in the lungs - hence there is a version of the drug in Viagra (Sildenafil) that treats arterial hypertension by increasing blood flow in the lungs.

Viagra wasn't designed to treat erectile dysfunction initially. It was supposed to be used to treat conditions like hypertension where the lungs were struggling to get enough blood to oxygenate.

The fact that it helps with erectile dysfunction was an unwanted side effect that they were able to capitalise on and market to men who can't get erect without it.

drugs are weird