Firmware will not download

I have an Arducopter V2.8

Assuming you mean an old APM 2.8 I took one of those out of the junk drawer and it flashed Plane V3.4.0 (last supported version) no problem with the latest Mission Planner Beta.

I got the latest Mission Planner as well (from http://ardupilot.org/planner/docs/mission-planner-installation.html). It does not work either. I reset the APM and rebooted MP several times, but there was still no change. The connection is fine, too (USB/haud rate: 115200). Mavlink was disconnected, when I tried to flash it. Have no idea.