[ProtegeManiac]

connect the red & white plug to the amp and the black plug into the desktop headphone output?

No, use the Front Left/Front Right combo jack on the motherboard/soundcard.

 

[PurpleAngel]

how do you connect a magni 2 to a desktop?

Motherboard's on-board audio normally comes with a combo Headphone/Front speaker jack (green, 3.5mm).

For the on-board audio to feed the best possible analog audio signal to the external headphone amplifier.
Set on-board audio to 2-channel and "Speaker" out, not "Headphone" out and max (75%-100%) out the on-board audio's volume controls.