Reverse Engineering an ERP interface written in Flash

Intercept the traffic between the browser / plugins and the server. I would start with Wireshark.

The traffic between the client and the server will be some form of network requests which you can write code to generate / consume.

My college has its erp platform in a flash interface, accesible only via Internet Explorer. Thing is, accessing the erp from amything other internet explorer results in the browser download a flash file "campus-lynx.swf". This means the platform is locked to windows only.

You are obviously wrong. Application work in firefox without any problems. Even site itself state "Best Peformed With Mozilla FireFox Version 2 and above".

Most recent Firefox versions start dropping Flash support, that may be the case. But you always can install portable version of Firefox 52 without this issue.

Judging by controls look and feel the application was build with Adobe Flex Builder.

There was several commercial Flash decompilers such as https://www.eltima.com/products/flashdecompiler/ You can try to decompile SWF file to figure out protocols being used.

Most probably there is something standard such as XML or Action Message Format.

UPD: Network activity tab in browser clearly indicate usage of AMF protocol. There is a plenty of AMF support libraries for various programming languages. Google it.