What backup systems are in place for flaps actuated by sliding block guides?
Given the footage in that video (rotating shafts rotating a jackscrew) There are 2 main failure modes I can think of: the linkage to the jackscrew fails or the jackscrew itself fails.

If the linkage fails the flaps will just not work. Jackscrews will hold the position of the flaps making the flaps fail up (not extended). There should be a feedback mechanism to stop the operational set of flaps before the asymmetric flaps affect the flight.

The jackscrew itself is engineered to not fail if properly maintained. There are also multiple jackscrews per wing

When flaps fail up the plane can still land. It just needs a much longer runway to account for the higher landing speed and a brake inspection. For example in this incident a Boeing 737-800 landed (almost) normally.

When flaps won't retract after takeoff the crew will circle back to the airport and land again with the flaps in takeoff position. This is somewhere between flaps full up and flaps in normal landing configuration.