How to flash an ATMEGA2560 using a WIZnet 5500?
The latest Ariadne bootloader from 'codebender' is in his 'personal' GitHub repository. It has W5500 support. Per created his fork with better documentation and a hardware package earlier. The loathingKernel's repo still lacks good documentation.

I installed Per's Ariadne package over Board Manager and then I replaced the files in Per's package with files from loathingKernel's repo. The I flashed the bootloader to Mega without problems and the Ariadne bootloader worked for me over W5500. 

I configured the upload from IDE too.