Do NOT install any program that claims to remove it.

Your Flash is NOT out of date, do NOT download the so called Flash installer. The only place to get that from is the website. Accept no substitutes.

As the procedure that you will find at
is long, but not necessarily difficult, I would advise you to read through the instructions a couple of times before you attempt it. PRINT it out, you will need to close Safari at times during the procedure.
Remember, this is a MANUAL remove, do NOT install any program.

Before you do any of the above, open Safari and go to preferences. On the General tab, find the check box that says "Open "safe" files after downloading". This will prevent any app from launching and installing without your say so.

Good luck and let us know how you get on.