I was trying to upload a photo on facebook using a browser with no flash, and could see that it didn\'t work.
I am pretty confident in handling files and related issues
It isn't a choice between Flash and PHP. You need something on the client to send the data and something on the server to receive it.
Ask yourself the following question:
Does Flash offer anything useful for my project?
The obvious things it lets you do are having a nice UI for selecting multiple files at once, and a simple method for seeing the progress of uploads.
If you decide that it does offer features, then implement it using progressive enhancement. Flickr is an example of this — with Flash you get the fancy uploader, without it you still get a series of regular file inputs. They aren't as nice to use, but they are functional and what would have been used if Flash wasn't an option in the first place