I have a bunch of animations that I have saved on Adobe Flash Professional CC, and I was wondering If I could somehow import the animations as an asset to Unity?
Yes. You have two options:
The cheapest is to use something like uniSWF. This will basically make images out of your swf animation, so it’s very simple but takes a lot of memory.
The more expensive solution is to use Scaleform. This essentially embeds a fully functional flash player into Unity, which is awesome, but it costs several hundred dollars per seat to license.