Portable charger recommendations for ASUS X550JX-DM321D laptop?

new notebook? best don't buy any additional trash ... extending battery life is best done with power saving settings
only if you really require an extended battery life due to circumstances you might wan't to consider a real secondary
lithium-ion notebook battery - can't recommend any portable chargers for notebooks

that battery-bank in the link with 5V/1A/2.1A doesn't even have enough AMPS
to charge/sustain power for any average 65V/3.5A notebook (properly)

I recently bought a "Jackery Giant+ 12,000 mAh" for my smartphone. I don't know if you can use it on a laptop but it works great on mobile devices.

yeah, i don't think that'll be happening.. those portable power banks are (almost) always limited to charging USB devices. (i have seen a few that can actually jump-start a car, but that's about it)
you'd be better off just having an extra battery for the laptop - http://www.amazon.de/Akku-für-Asus-X550JX-1A-38Wh/dp/B013Y5ZZXE/ should work (although you will have to shutdown to replace it, of course)

The PowerAdd Pilot's specifications seem to indicate it can output a maximum of 90 watts (20V/4.5A) so on the DC port so it should put out enough for your 65 watt laptop. Looking on Amazon there are a lot of very similar models under different brand names and one explicitly says 60W max (which would still be enough). It also supports 19v output which your laptop seems to need, but the tricky question is whether the included plug adapters will fit your laptop's port. They at least seem to indicate ASUS compatibility.

It seems your laptop uses 4x 18650 cells in its battery pack with 3000mAh cells (44Wh/14.8v=2.973Ah). The PowerAdd Pilot is approximately equivalent to 2.5 of those batteries in capacity (32000/3000=~10.6) but there could be losses of up to around 20% due to the voltage conversion to 19v and the laptop feeding some of the power back into its internal battery. Assuming it's true to its specs, your battery life should be somewhere between 300-350% of what it originally was when connected to the Poweradd Pilot.