It is important for every musician, not just a jazz player, to know that scales and chords represent one another. To think of a chord should be to think of that scale. This is true if the chord is simple; say a C major triad, or complex, like a C altered dominant. If one breaks down chord and scale relationships, at the most elementary level, both could be seen as working with numbers. Every degree of the scale and every chord tone are associated by a number; the root is one, the third is three, etc. When you practice scales, chords and arpeggios, try to hear each scale degree and think in terms of these numbers. This is especially helpful when practicing all twelve keys on your instrument. Instead of having to think individual notes, try to hear numbers. When visualizing music on your instrument, think numbers as opposed to individual notes. A good musician should also be able to name the notes of the chord or scale that they are trying to play. As you practice chords, remember that the notes in the chord are also in the scale you use to improvise, and when you practice scales, remember that a chord change goes with those set of notes. Practice the scales up and down, on the full range of your instrument, and practice arpeggiating all the notes in the chord. Think of the scalar sound as being heard horizontally and the arpeggiated chords as vertical uses of the same set of notes. Just playing scales and chords can be boring though, so mix it up with scalar patterns, arpeggiating in fourths and fifths, playing different modes of the scale as you ascend and descend, etc.
Being able to hear scales and chords is important, but as you improvise try to think melody. A good starting place is to have the melody of the tune in your head as you improvise. This helps your thinking as you improvise, and helps you to keep track of the form of the tune as you play. Eventually one will be able to recognize music without having to think notes. You will begin to feel the music instead of thinking notes and numbers.
As always, happy practicing!