If Adobe says that it won't work on your computer, then it's probably best to listen to Adobe and ignore the update suggestion.

Firefox just knows that there is a newer version of Flash so it's telling you that it's out there. At this point, you are likely to begin (if you aren't already) to start running into incompatible updates on a more regular basis since your operating system is over 10 years old. I'm not saying that as an insult or anything, just an observation.