I can't get Skype and Jack working together on a debian Wheezy,
2.6.39-2-amd64. The goal is to have them working in order to stream
telephone calls with IDJC but none of the misc solutions I tried seem to
work, including the one found on IDJC project page.

When qjackctl is up and running, skype audio doesn't work (no capture no
playback).

Any suggestion is appreciated

I've had problems with the alsa loopback metheod with Skype since they added pulseaudio support. The only reliable solution I've found is using the pulse-jack bridge written by Falktx from kxstudio. Not using pulseaudio obviously rules this out. Other report that it works fine though so your milage may vary.

Dan