How do you think of this one from Kenny Garrett (just the A section, B only makes a brief appearance) - functional chords or no? 3 major chords, each a step apart, the bass outlines the triads, and the melody moves from A (over Esus) to G (E minor) over the D. Garrett plays all kinds of stuff over this - close to the melody, blues, and an eastern-sounding scale at the end (g#,a,b,c,e,f#).
Since the E triad is established both through Qualitative Emphasis (placed in prominent places such as phrase beginnings and endings) and Quantitative Emphasis (used the most often and occupying the greatest number of beats) as the Tonic chord, the D chord actually functions tonally as bVII (Subdominant Minor), and the C as bVI (also SDM). This vamp could be viewed as a short progression in E Major--or on the Composite Scale on E which results from combining what everyone is doing, the following Octatonic Pitch Collection: E F# G G# A B C D E.
In short, a Non-Functional Chord Succession is a series of chords in which no consistent tonal functionality is evident. This is a vamp on E, but with some limited functionality. Bassist Nat Reeves (an old friend) plays the chord tones of each triad in open position, which is doubled at the octave by the pianist's left hand (a powerful device much exploited by Horace Silver).
21st century vamps can demonstrate tonality, modality--or not (can be non-functional--even atonal). These chords, if arranged randomly (and mixed up in their repetition in such a way as to destroy the feeling of tonality, would be both non-functional and Atonal (without primary key): C E D C D E, for example. On the other hand, if you apply either qualitative or quantitative emphasis to any one of them, it becomes the priority chord. Therefore, even non-functional successions can either sound a priority chord or not, depending on how the chords behave. Here's a solution that would be both non-functional and based "on" C: CDC CDED CED CDC C.
Scale and pc possibilities are huge. Beyond that is the kind of Motive Transposition (motives drawn from the Exposition line) and developmental devices as found in my LJI Polytonal Triad Etudes book: motive transposition, retrograde, mirror, augmentation, diminution, displacement, permutation, fragmentation, mix-and-match, palindrome, and much more. The more the background harmony exhibits a state of stasis, the more it invites the soloist to explore lead lines which create linear chord successions (or the sense of harmonic forward motion), in styles in which the chord accompaniment does not.
From the excerpts I hear above in the solos on this piece in question, however, while the pianist employs quartal harmony and their related pentatonic scales which he side-slips (in addition to playing on the prevailing pc), KG instead bases his improvisation almost exclusively on the Melody PC (an LJI term), which is also comprised of the composite scale mentioned above. Nothing is ever ruled out, of course, as both soloists feel free to employ F and other non-harmonic tones for Chromatic Targeting in order to create melodic tension to propel the line forward. The F happens most frequently in this regard, acting as a b2 (ra) chromatic upper neighbor (LJI Targeting Type 1b).