Can't find any reliable sources about their clothes and curious from where did it come. Did roman/greek sources describe their clothes in such manner or historians somehow were able to find a remaining pieces with such patterns?
There's always more to be said, but in my answer to What (specifics) do we know about clothing of Northern/Central European men during the late Bronze- / early Iron-age? I discussed archaeological and textual evidence for Celtic clothing of this period. One way that we know they wore checks and stripes is that they appear in the tiny textile fragments that have survived.