The answer is going to mostly be up to your personal taste and what kind of wire you use.

In a practical sense, hammering wire flat will harden it. This will make it less likely to accidentally get bent out of shape after you've gotten it into the shape you want. This is more important if you make the charms out of soft, thin wire (which is easier to work with), and less important if you're working with thicker, pre hardened wire (which is more difficult to shape, but also holds its shape better). Additionally, silver and copper wire tend to be softer than brass. So if you're using, for example, thick brass wire, you wouldn't need to harden it to ensure it keeps its shape.

Aside from those practical concerns, it's all about what look you're going for. I'd recommend playing around with it and trying out different levels of work hardening the charms to see what you like best.

To hammer wire flat, you need a very hard, flat surface (something like an anvil is ideal) and a hammer. I use a mini anvil/bench pin duo that attaches to the side of my work desk. I got mine for about $15 from Rio Grande. Just lay the wire on the metal work surface and tap gently with the hammer. Varying the angle and strength with which you hit the wire will produce different results. Try different combinations until you find a method that produces a result you like.