Each browser has a different plug-in scheme:
Internet Explorer uses ActiveX controls, and the ActiveX version of Flash Player is specific to IE.
Firefox uses the Netscape Plugin API (NPAPI), and the Plug-In version is specific to Firefox and other NPAPI browser
Chrome uses the PPAPI (Pepper Plug-In API) and PPAPI Flash Player is specific to Chrome and other Chromium-based browsers.
They're mutually exclusive and do not interoperate beyond reading from some central file stores in the case of the ActiveX and NPAPI Flash Players. PPAPI is completely encapsulated.
Let's take a more structured approach here. The following information, specifically a description of the crash and how to reproduce it would be useful to get started: