Martin, on p. 29 of "All about your kilt" (I'm paraphrasing, btw) states that it is possible to wear a "hounds-tooth [day] jacket, a tattersall-checked shirt, and regimental stripe tie, whilst an American will usually wear solid-colour accesories with the kilt."

Martin then goes on to state the key to mixing patterns and colours is toning -- as long as the patterns and colours "tone" with each other, then there is no clashing. Size of the pattern also matters; a tattersall or Glen Plaid dress shirt, for instance, must have a smaller pattern than the the tartan itself.

Bottom line: like so many other ways to wear the kilt, it is really up to individual style.

Cheers,

T.