The standard installer for any generic linux desktop, located at
http://calibre-ebook.com/download_linux
Since as you say your Synology is an Intel i686 version, just pretend it is a headless desktop and install calibre as normal.
If you
want to build calibre from source, even on i686, then feel free to indulge in that hobby horse. I do.
But it isn't *necessary* unless you intend to run calibre on an ARM processor.
It really is as simple as: no one has compiled the standalone version for ARM, and trying to install the version compiled for Intel i686 on an ARM processor is a fool's endeavor, no less than installing 64-bit code on an i686 processor.
A Synology is more or less a standard linux computer with a custom distro and no monitor attached.