In the meantime I found this explanation of the setup on Windows 10, with temporary disabling of Driver Signature Enforcement, allowing you to install the right drivers.
http://www.droidviews.com/setup-andr...vices-windows/

He also gives a step-by-step guide for XperiFirm and FlashTool.
http://www.droidviews.com/install-st...and-flashtool/

Edit: I finally flashed the phone. Thanks guys!
The trick for me was the installation of the drivers. Everything seemed to be OK, but apparently wasn't. The part of disabling of Driver Signature Enforcement before starting Flashtool-drivers.exe was crucial. I only installed the upper two drivers. All the others are meant for specific models, and the X is not among them.

Further newbie tips: on the phone, Settings, About phone, click "Build number" until you are a Developer. With Developer Options allow "USB Debugging". I disabled "Verify apps over USB", not sure whether needed. For later use, enable "OEM unlocking" here too.

Before flashing: hold key Volume Down when plugging in the USB cable. For backupTA connect normally with MTP.