Hello, I was wondering if you could replace using flash with a program called Vectorian Giotto. I would appreciate any advice.

Never heard of it. You might be able to use it, but we wouldn't be able to help with more than standard animation advice.

i don't know what device you are using to animate

Vectorian Giotto is more for making advertises as far as I know, but the layout is pretty similar to Flash. I think it would be a good software to start with.

Vectorian Giotto is flash. It's free and the smoothing system is less then crap, but it works and is good practice before you buy a better program. And as for the videos you've seen, it isn't a very popular program so it's unlikely that you'll see any professional videos using this program.
Trust me. It is better than pivot