It's relatively safe.
Flash has ALWAYS been plagued with security issues because a) IMO it's always been poorly written, and b) it is a plug-in that requires access to many system resources in order to work (like Java) and thus is a good attack vector (like Java) for malware writers.
Adobe does their level best to stay on top of the threats. As long as you keep up-to-date with the latest version (Software Update will NOT take care of this for you), you should be at very low risk of problems.
You can get the latest version for your machine from here:
Adobe - Install Adobe Flash Player
Being on Snow Leopard, running the latest version of Flash is important if you're going to run it at all.
As for Google Chrome, IMO it has two problems:
1. It has Flash built in, and may not always be up to date compared to what Adobe has put out. Usually the Google team update it quite frequently (TOO frequently!), so this may not be much of an issue.
2. The purpose of Chrome -- like most other Google services -- is to gather information on what you do online so that Google can sell that information to advertisers. IMO -- not shared by everyone -- it is akin to fairly benign spyware, albeit not for a particularly sinister purpose. It's a fast, nice browser, no question about it. It just has a not-so-hidden agenda that I don't think Firefox or Safari (et al) share, and doesn't offer me the control over what I share and don't share that even Facebook (a company with the
exact same business model) offers me. Again, just my two cents. Feel free to picture me with a tin foil hat on if it helps.