The installation of an always up to date Kontact should be available now as a flatpak. THANKS FOR THIS (and looking forward to maybe also find a snap version soon?).
However, installation does not really work by now. In the following you will see that a first installation attempt failed because of a serve side error (Bad Gateway) and only some of the necessary flatpak parts became installed. But in a second attempt, when the server answered correctly and the missing flatpak part should have been installed, it failed with a KDE Kontact flatpak package related error message. In a third attempt, another odd error message was thrown, before in a fourth attempt the second (KDE KOntact related) error was on again. I have had ti give up after a 5th try, which throwed another odd error message. Hope this feedback helps to get the flatpak offer polished:

On Debian 9 (Stretch, stable, amd64):
# apt install flatpak
# flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo
# flatpak install flathub org.kde.kontact                                                
Required runtime for org.kde.kontact/x86_64/stable (org.kde.Platform/x86_64/5.11) is not installed, searching...
Found in remote flathub, do you want to install it? [y/n]: y
Installing: org.kde.Platform/x86_64/5.11 from flathub

12 delta parts, 112 loose fetched; 315878 KiB transferred in 57 seconds                                                                                                                                                     
Installing: org.freedesktop.Platform.ffmpeg/x86_64/1.6 from flathub

1 delta parts, 3 loose fetched; 2650 KiB transferred in 1 seconds                                                                                                                                                           
Installing: org.kde.Platform.Locale/x86_64/5.11 from flathub

6 metadata, 1 content objects fetched; 15 KiB transferred in 1 seconds                                                                                                                                                      
Installing: org.kde.kontact/x86_64/stable from flathub

Receiving delta parts: 0/3 6.6 MB/s 6.6 MB/41.2 MB 5 seconds remaining                                                                                                                                                      
error: While pulling app/org.kde.kontact/x86_64/stable from remote flathub: Server returned status 502: Bad Gateway


# flatpak install flathub org.kde.kontact
Updating: org.kde.Platform/x86_64/5.11 from flathub
No updates.
Updating: org.freedesktop.Platform.ffmpeg/x86_64/1.6 from flathub
No updates.
Updating: org.kde.Platform.Locale/x86_64/5.11 from flathub
No updates.
Installing: org.kde.kontact/x86_64/stable from flathub

1 delta parts, 1 loose fetched; 1736 KiB transferred in 1 seconds                                                                                                                                                           

(flatpak install:21273): flatpak-WARNING **: Non-prefixed filename org.freedesktop.Akonadi.Control.service in app org.kde.kontact, removing.
error: No such file or directory


# flatpak install flathub org.kde.kontact
Updating: org.kde.Platform/x86_64/5.11 from flathub
No updates.
Updating: org.freedesktop.Platform.ffmpeg/x86_64/1.6 from flathub
No updates.
Updating: org.kde.Platform.Locale/x86_64/5.11 from flathub
No updates.
Installing: org.kde.kontact/x86_64/stable from flathub

2 metadata, 0 content objects fetched; 569 B transferred in 0 seconds                                                                                                                                                       
error: While pulling app/org.kde.kontact/x86_64/stable from remote flathub: Update is older then current version


# flatpak install flathub org.kde.kontact
Updating: org.kde.Platform/x86_64/5.11 from flathub
No updates.
Updating: org.freedesktop.Platform.ffmpeg/x86_64/1.6 from flathub
No updates.
Updating: org.kde.Platform.Locale/x86_64/5.11 from flathub
No updates.
Installing: org.kde.kontact/x86_64/stable from flathub

1 metadata, 0 content objects fetched; 569 B transferred in 0 seconds                                                                                                                                                       

(flatpak install:21514): flatpak-WARNING **: Non-prefixed filename org.freedesktop.Akonadi.Control.service in app org.kde.kontact, removing.
error: No such file or directory


# flatpak install flathub org.kde.kontact
error: GPG signatures found, but none are in trusted keyring