You're allowed to wear water shoes so I don't see why not. They don't really allow you to wear flip flops because they can fly off. It just depends on if they enforce that. Seeing that these strap on, I imagine they're fine
Some slides do require that you hold them in your hand, including water shows. Anything with "traction" (so rubber soles) must be taken off on body slides. If it is an inner tube slide you can leave them on. The lifeguard/ride operator will instruct you as needed.
I would recommend wearing aqua shoes at the water parks (very reasonably priced at Walgreen's or CVS). You can wear them everywhere, even the wave pool, and they only asked me to take mine off for one slide.