As of last year, Adobe issued a statement saying they were no longer going to continue developing Flash for mobile devices, however, it may still be further developed by other individuals. The reason for this has to do with HTML5 (mostly functional, not fully functional yet though). Bottom line is, you may be able to access chat from your Nokia phone if your phone supports a Flash plug-in you can download and the necessary version of Flash for chat. PC's coding is a bit older in that it still uses HTML4 and supports older versions of IE, so it probably won't need a very new Flash version.

Many Nokia models support Flash, so chances are yours will as well.