Installation as such works out of the box.
Once all the prerequisites are also installed (see below, What does not work section), most of the things work.
What does not
Installing in a brand new and empty wineprefix finishes with launching the application, which then hangs. Workaround: install fonts  (I am not sure whether this actually helped or not), wine-mono-4.6.4  (also not sure if this step was necessary), Microsoft Visual C++ 2010 SP1 Redistributable Package (x86)  and jre-8u40-windows  (installation complains about unsuccessful install, but works nevertheless; newer versions fail to install )..
Resizing the app window using window manager leaves the app hanging (BUT window resizing works from within the application: buttons "Scale Up" and "Scale Down"; the window manager in question is xfce and has not been observed to misbehave).
Choosing a typeface when emulating Fire devices: only Georgia appears in the fall-down menu and Georgia is used to render the body text (not publisher default).
During this testing the app froze twice for no apparent reason.
 using winetricks
 http://ftp.psu.ac.th/pub/java/jre-8u40-windows-i586.exe or http://ftp.psu.ac.th/pub/java/jre-8u40-windows-x64.exe
What was not tested
I'm actually using wine-1.9.23 (Staging). winetricks 20140817 - sha1sum: fb1d7184dc186313cf26e1a65a8e6ff3c5fadc50 md5sums of installers acquired: 2caa6c9141f2bb1769203b67e6ac9eed KindlePreviewerInstall.exe 59c093f4f6fe80744bda263bb7c414ab jre-8u40-windows-i586.exe e6c7a0ccb3701588ef3d67b5ce4bdcd9 jre-8u40-windows-x64.exe cede02d7af62449a2c38c49abecc0cd3 vcredist_x86.exe b0760cf51527b70435c3e4d0361a129a wine-mono-4.6.4.msi
|Operating system||Test date||Wine version||Installs?||Runs?||Used|
|Current||Debian GNU/Linux 8.x "Jessie" x86_64||Jan 07 2017||1.9.24||Yes||Yes||Bronze||Darki|