How is it possible to perform a chromatic glissando in a fast passage on a harp, as in the example below?
On the common pedal harp- not very quickly. The harp does not have a string for each chromatic note; rather, it has one string for each note in Cb major, and the pitches of strings can be altered with pedals to play any note in any key. You can't have more than 7 notes per octave immediately accessible, so a chromatic glissando like the one shown in the question would require the player to alter and re-strum several individual strings very quickly. Not viable.
If you want the glissando to sound atonal, you may try starting with a glissando through the notes of Cb major only, and adding some sharps so that many of the notes fall outside the key of the piece.
Alternatively, you can require the player to use a multi-course harp which is truly chromatic.