It seems most are in agreement - at least in the formative stages, students are better to develop the attitude that they are using "register keys" to facilitate octaves, eliminate split notes and croaks etc.
"Flicking" as a term and concept came from a time when it was almost accepted that bassoons cracked notes and generally played rather coarsely - you could see the apprehension in visiting conductors' faces as they began rehearsing some orchestras.
The practice was not unique to bassoons either - horns, oboes, often other woodwinds, trombones in community orchestras were often self taught and played to fill a vacancy. We had to work hard at establishing a quality approach to intonation, tone, ensemble etc but as time went by standards lifted and players more often got to study at a tertiary level. And groups like IDRS lifted performance practices enormously - and still do.
I would introduce "flicking' at later levels of advanced technique insisting that zero "splits" must be guaranteed. Rapid passage work keeps the reed vibrating in the upper harmonics so the movement can be reduced at speed. However in exposed and held notes if in doubt use the register keys.
As a guide - on "standard layouts
the first register key is used for A and can be used on most bassoons for Bb too.
the second register key is used for Bb B & C and high B C
the third where fitted is for high C# D D# (high notes require held venting - no flicking)
At senior levels, more sophisticated reed preparation and profiling, alongside an intimate knowledge of your instrument, may give confidence in reducing the use of register keys in many situations, but quality must be the over-riding determinant.
Christchurch New Zealand
Bassoonist / Teacher / Conductor