The port generally aims follow upstream chromium checkout procedures. It means you need to have chromium depot_tools checked out somewhere and added to your PATH (https://www.chromium.org/developers/how-tos/install-depot-tools). If you have that, to get the code it should be enough to run the following commands:
$ mkdir chromium-qs $ cd chromium-qs $ gclient config --name src/qt_port https://github.com/tworaz/quicksilver.git $ gclient sync
The checkout may take a while. After it's finished you need to apply some patches to the chromium source tree:
$ cd src $ git am qt_port/patches/*
To build the code on desktop it should be enough to run:
$ ./qt_port/configure $ ninja -C out.qt.x86_64/Debug content_shell quicksilver_shell
To run it just execute: $ ./out.qt.x86_64/Debug/content_shell --no-sandbox or $ ./out.qt.x86_64/Debug/quicksilver_shell
On desktop the code needs at least qt 5.4 to run under X11. For wayland support you need to upgrade to 5.5, or patches to qtwayland a bit.
Building the code for SailfishOS is a little bit more problematic. First you need to patch Qt a bit (I'll need some time to cleanup the patches and push them somewhere), second you need custom Sailfish SDK build which provides gcc 4.8. Unfortunately the default GCC 4.6 is too old to compile chromium m44, or even m40. From what stskeeps told me Jolla plans to move to 4.8 in the near future.