is the nikon d3200 goos for skateboarding photography?

Sure, any dslr is capable of great skateboard photography. The choice of lens is far more important than the camera body. How you want to capture the shots is up to you, but most use normal and superwide lenses for skate photography. What's your budget? I can give some suggestions if you want.

It's ok but I prefer the D5200 with the hinged screen.

Almost any camera has fast enough shutter speeds for skateboarding.

I would set it to the fastest shutter speed for flash sync and use fill-in flash to fill in the shadows. You could also experiment with using flash at lower shutter speeds. You can get some interesting effects that way.

As for lenses, I would go for anything between 24mm and 50mm (equivalent to about 16mm and 35mm on full frame cameras) and get in as close as you can, bearing in mind that flash (I think) will only go as wide as about 36mm.

So I would use either a 35mm fast prime or a zoom around 24mm to 50mm or close to that.

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Look at a go pro, they're far smaller and cheaper.