Question [Q] Howto gain root with Linux?

Hi,
I'm looking forward to getting my Z1 tomorrow, and being used to having root on my device (ever since I jailbroke my iPhone 3GS) I'd like to get it here as well.

After a bit of reading I got the impression it's rather difficult compared to my previous phone - at least when I'm not having access to a windows computer.
So far I found that Flashtool will be able to unlock my bootloader - but will that be enough to flash SuperSU.zip in order to gain root?

Or is there some other way I overlooked so far? Please help an Xperia noob to make the first steps safely

I appreciate all advice, links, ...

Device: Sony Xperia Z1 (C6903 aka honami)
Recovery: TWRP v2.6.3.0
ROM: SlimKat latest weekly (Android 4.4, CAF stuff included)
Modem: 8974-AAAAANAZQ-10270047-39
Kernel: 3.4.0PIMPED+-gf79222f-dirty

Previous phones: HTC Incredible S (vivo), Samsung Galaxy S3 LTE (i9305)