How to prevent voltage regulator board heating up and how thick traces should be?
Trace thickness is the thickness of the copper layer.  In the US you order that by "ounces", which really means ounces per square foot.  If your calculator wants the thickness in mm or inches, look up the conversion.

Just to complicate things, you can order different copper thicknesses.  The typical thickness is 1 ounce, and it's common to get thicker copper.  If you're buying from a PCB aggregator, then you're going to get what they supply (probably 1 ounce).

You're concerned with the trace width, which hopefully you now have enough information to figure out.

I strongly suggest that you look at the layout guidelines on the datasheet.  Switching supplies like this have high-current, high-frequency signals on them, and layout is not trivial.  You need to think about where the current is going to go during each phase of the switcher's PWM cycle, and make sure it can get there.  Starting with TI's layout example is a really good idea.