Use a steady motion of down and up strokes; down strokes on the beat and up strokes in between.
Make it sound relaxed, lazy even, with a swing feel.
Every chord on the one is preceded by a guiding chord 1 fret below.

The 9th chords in the last bar can also be played in a form that doesn’t have the tonic on the bottom, but the fifth of the chord.
Some swing players prefer these forms, since you already have a bass player who’s playing the tonics. Why bother?
If your hands are big enough, you can try to play the tonic of the Bb9 chord with your thumb.

Note: This laid back timing can be practised by making big circles parallel to the strings.
Hit the strings near the neck of the guitar with down strokes and play near the bridge when you play up strokes.
Once you get into the feel you can make the circles smaller.
Make it sound like you’re always a bit too late.
Try to feel where the beat is and experiment with your timing.

Damping is an important part of playing rhythm in swing.
Because we don’t usually play full bar chords, we can’t dampen by just lifting our left hand.
With some chords we’ll dampen the open strings with the side of our fingers.
Sometimes we’ll have to dampen with the right hand. Use your palm to stop the strings from ringing right after you play a stroke.

Varying these damping patterns will give you different grooves.