The terms pan-tonal, non-tonal, and atonal all describe the blurring or elimination of traditional tonality. The distinction between these terms is not always clear, so I will use most general of these, “non-tonal”, to describe music that has no specific key center, or over which standard chord/scale relationships do not always apply.
Although non-tonal music may appear to have chord progressions, the individual chords are often chosen for their overall sound rather than for their resolutions. Any chord from any key is likely to be used if it has the right sound. For example, many of the tunes on Miles’ albums E.S.P., Nefertiti, Miles Smiles, and Sorcerer have no specific key centers, nor do they contain many traditional ii-V’s that would indicate temporary key centers. Many of the chords are relatively complex, for example Abmaj7#5, and each chord is chosen for its individual sound, not because the previous chord resolves to it naturally or because it resolves to the next chord. A traditional functional analysis of the harmony (that is, analyzing chords in terms of their relationship to the key) is not always the best way to approach this sort of music.
You may wish to treat this music modally, and let the chords themselves dictate the scale choices. You should be careful in doing this, however. Many of the standard chord/scale relationships were established with traditional resolutions in mind. Your phrases may seem random and disconnected if you blindly change scales according to the chord progression in non-tonal music. You should be prepared to treat the chord/scale relationships more loosely than you would when simply playing changes.
In tonal music, alterations to a chord are often considered merely color tones that do not affect the basic function of a chord, and improvisers are free to make their own alterations to the basic chord. For example, a G7b9 chord is likely to be a dominant chord, resolving to Cmaj7. Any other chord that serves this function, such as G7#11, or even a tritone substitution like Db7, can be used instead without radically changing how the phrase is perceived, so tonal improvisers will often make this sort or alteration freely, either explicitly, or implicitly by their scales choices. In non-tonal music, however, a chord is often specifically called for because of its unique sound, and not because of how it functions in a progression. The same G7b9 chord may have been chosen because of the particular dissonance of the G against the Ab, or because that happened to be the most convenient way to spell the chord voicing the composer intended (a voicing is simply a way of specifying the particular notes to be played for a given chord). Changing this chord to G7#11 may change the sound of the chord more radically than substituting an otherwise unrelated chord that has the same G/Ab dissonance, such as Abmaj7, or one that may be voiced similarly, such as E7#9. You may find scale choices associated with these chords to be more appropriate substitutions than ones based on the traditional dominant function of G7b9.
The real intent of non-tonal music, however, is to free you from the specifics of chord/scale relationships and allow you to concentrate on the sounds themselves. The lines you play need not be analyzed in terms of their relationships to the notated chords, but may instead be thought of in terms of how they fit the sound of the phrase at that point. If the chord in a given measure is a maj7#5 chord, then you should hear the sound of that chord, and feel free to play any lines that imply that sound. This is as much an emotional implication as a rational one. For me, that particular chord has an open, questioning, sound that I associate with wide intervals and the use of rhythmic space. I would probably tend to play lines that reflect this feeling, regardless of the actual notes involved. Furthermore, the sound of that chord may also be affected by its context in the piece itself. For instance, a chord played for two measure in a ballad may sound entirely differently from the same chord used as an accent in a driving up-tempo piece. Chord scale relationships may still help define which notes tend to be more or less dissonant against a given chord, but you should try organize your thinking along lines of sounds, and use the chord/scale relationships only as tools to help you achieve the desired sounds.
Even in tonal music, of course, chord/scale relationships can be considered as tools, and one could claim the goal is always to represent sounds. However, you may find tunes with many ii-V’s in them tend to “sound” the same in this respect. Non-tonal music was created to provide a more varied palette of sounds, to encourage thinking along these lines. As with chromaticism in tonal music, you can deliberately play lines that contradict the sound of the chord, if that is the effect you desire. The important thing is that you perceive a non-tonal chord progression as a recipe of sounds over which you improvise, not as a specific pattern of chord resolutions.