After some search it appears that to use Jack with PortAudio you need the library jack_portaudio.so
No all Linux distribution gives jack_portaudio.so by default, maybe you have to check if your distro give it.
You may also try to use Jack and PulseAudio (PortAudio can deal with PulseAudio).
To have it, just install qjackctl and pulseaudio-module-jack module:
sudo apt-get install qjackctl pulseaudio-module-jack
Then configure qjackctl to run the following command after startup. Copy it into "Setup..." > "Options" > "Execute script after Startup":
pactl set-default-sink jack_out
And that is.
Pulseaudio will recognize (through D-Bus) that JACK started, and automatically will route audio to it. When JACK is stopped Pulseaudio will revert to normal routing and start sending audio directly to card again.
So (almost) by default Pulseaudio implements the setup detailed above by mmv-ru.
Otherwise you should compile Jack and enable flag to enable jack_portaudio.so compilation.
See more details here: