Rather sketchy advice, i am afraid!
On adobe sh*t always look for the verbose output to quickly look for errors.
root@asterix:/home/micha# update-flashplugin-nonfree --install
root@asterix:/home/micha# update-flashplugin-nonfree --install --verbose
options : --install --verbose --
temporary directory: /tmp/flashplugin-nonfree.ACDT3Uv2vN
importing public key ...
selected action = --install
installed version = 11.2.202.521
upstream version = 11.2.202.540
wgetoptions= -nd -P . -v --progress=dot:default
downloading http://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp.11.2.202.540.sha512.amd64.pgp.asc ...
--2015-10-16 11:26:50-- http://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp.11.2.202.540.sha512.amd64.pgp.asc
Auflösen des Hostnamens »people.debian.org (people.debian.org)« … 5.153.231.30, 2001:41c8:1000:21::21:30
Verbindungsaufbau zu people.debian.org (people.debian.org)|5.153.231.30|:80 … verbunden.
HTTP-Anforderung gesendet, auf Antwort wird gewartet … 301 Moved Permanently
Platz: https://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp.11.2.202.540.sha512.amd64.pgp.asc [folgend]
--2015-10-16 11:26:50-- https://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp.11.2.202.540.sha512.amd64.pgp.asc
Verbindungsaufbau zu people.debian.org (people.debian.org)|5.153.231.30|:443 … verbunden.
HTTP-Anforderung gesendet, auf Antwort wird gewartet … 404 Not Found
2015-10-16 11:26:50 FEHLER 404: Not Found.
wget failed to download http://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp.11.2.202.540.sha512.amd64.pgp.asc
downloading http://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp10.sha512.amd64.pgp.asc ...
--2015-10-16 11:26:50-- http://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp10.sha512.amd64.pgp.asc
Auflösen des Hostnamens »people.debian.org (people.debian.org)« … 5.153.231.30, 2001:41c8:1000:21::21:30
Verbindungsaufbau zu people.debian.org (people.debian.org)|5.153.231.30|:80 … verbunden.
HTTP-Anforderung gesendet, auf Antwort wird gewartet … 301 Moved Permanently
Platz: https://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp10.sha512.amd64.pgp.asc [folgend]
--2015-10-16 11:26:51-- https://people.debian.org/~bartm/flashplugin-nonfree/D5C0FC14/fp10.sha512.amd64.pgp.asc
Verbindungsaufbau zu people.debian.org (people.debian.org)|5.153.231.30|:443 … verbunden.
HTTP-Anforderung gesendet, auf Antwort wird gewartet … 200 OK
Länge: 1250 (1,2K) [text/plain]
Wird in »»./fp10.sha512.amd64.pgp.asc«« gespeichert.
0K . 100% 52,8M=0s
2015-10-16 11:26:52 (52,8 MB/s) - »»./fp10.sha512.amd64.pgp.asc«« gespeichert [1250/1250]
verifying PGP fp10.sha512.amd64.pgp.asc ...
copying /var/cache/flashplugin-nonfree/install_flash_player_11_linux.x86_64.tar.gz ...
verifying checksum install_flash_player_11_linux.x86_64.tar.gz ...
wgetoptions= -nd -P . -v --progress=dot:default -O /tmp/flashplugin-nonfree.ACDT3Uv2vN/install_flash_player_11_linux.x86_64.tar.gz
downloading https://fpdownload.adobe.com/get/flashplayer/pdc/11.2.202.521/install_flash_player_11_linux.x86_64.tar.gz ...
verifying checksum install_flash_player_11_linux.x86_64.tar.gz ...
unpacking install_flash_player_11_linux.x86_64.tar.gz ...
verifying checksum contents of install_flash_player_11_linux.x86_64.tar.gz ...
moving libflashplayer.so to /usr/lib/flashplugin-nonfree ...
setting permissions and ownership of /usr/lib/flashplugin-nonfree/libflashplayer.so ...
Flash Player version: 11.2.202.521
moving install_flash_player_11_linux.x86_64.tar.gz to /var/cache/flashplugin-nonfree ...
flash-mozilla.so - automatischer Modus
link best version is /usr/lib/flashplugin-nonfree/libflashplayer.so
Link verweist zur Zeit auf /usr/lib/flashplugin-nonfree/libflashplayer.so
link flash-mozilla.so is /usr/lib/mozilla/plugins/flash-mozilla.so
/usr/lib/flashplugin-nonfree/libflashplayer.so - Priorität 50
calling update-alternatives ...
flash-mozilla.so - automatischer Modus
link best version is /usr/lib/flashplugin-nonfree/libflashplayer.so
Link verweist zur Zeit auf /usr/lib/flashplugin-nonfree/libflashplayer.so
link flash-mozilla.so is /usr/lib/mozilla/plugins/flash-mozilla.so
/usr/lib/flashplugin-nonfree/libflashplayer.so - Priorität 50
removing /usr/bin/flash-player-properties
removing /usr/share/applications/flash-player-properties.desktop
removing /usr/share/icons/hicolor/16x16/apps/flash-player-properties.png
removing /usr/share/icons/hicolor/22x22/apps/flash-player-properties.png
removing /usr/share/icons/hicolor/24x24/apps/flash-player-properties.png
removing /usr/share/icons/hicolor/32x32/apps/flash-player-properties.png
removing /usr/share/icons/hicolor/48x48/apps/flash-player-properties.png
removing /usr/share/pixmaps/flash-player-properties.png
installing /usr/bin/flash-player-properties
installing /usr/share/applications/flash-player-properties.desktop
installing /usr/share/icons/hicolor/16x16/apps/flash-player-properties.png
installing /usr/share/icons/hicolor/22x22/apps/flash-player-properties.png
installing /usr/share/icons/hicolor/24x24/apps/flash-player-properties.png
installing /usr/share/icons/hicolor/32x32/apps/flash-player-properties.png
installing /usr/share/icons/hicolor/48x48/apps/flash-player-properties.png
installing /usr/share/pixmaps/flash-player-properties.png
end of action --install
cleaning up temporary directory /tmp/flashplugin-nonfree.ACDT3Uv2vN ...
end of update-flashplugin-nonfree
While the '--install' option does suggest success, the '--verbose' trigger unhides the failed download because of the poorly maintained
debian package. It usually takes a couple of days for the download link to be adjusted.
If you need a quicker solution, you need to go to adobe's page, download, extract and copy the content of their archive to the appropriate places.