Of course, all parrots can fly, so the question of whether they can fly away is an obvious yes, they can. But, more to the point, do they fly away, or will pet parrots fly away? Parrots are social animals, with their lives revolving around their flocks. The best thing is, if you have owned your parrot for a while, then you are part of that flock. Therefore, they will want to come back to you eventually, even if they do fly off. So, the first thing that you need to do if it looks like your parrot is about to fly away is to not panic.
If you are reading this before you find yourself in the situation, try to get a recording of the parrot making their calling noise. That will allow you to use the recording to lure them back to you, as they will hear their own voice. Also, remember to follow them as best you can, calling them. Parrots cannot fly for too long, as they are not used to it. So you are likely not to find them fly away very far. If you can, take your cage out with you when you are trying to retrieve your parrot, as they will know what it looks like and see treats in there.