"Jaké barvy jsou moje šaty?"

What makes you think "jaké barvy" is plural? I would interpret it as genitive singular. The nominative plural interpretation doesn't really seem tenable in Czech. The verb might be misleading you. "jsou" is plural because "šaty" is. That could correspond to either singular or plural in English, because English, unlike Czech, uses the singular when there's only one of them. But it doesn't tell you anything about the number of "jaké barvy".

Word color does have a plural form - it is colors. The expression "Jaké barvy" can be used in both forms, singular and plural. In this sentence is "Jaké barvy" in sigular. This formulation isn't very much used in the common speech but you can find it in literature and sometimes also in films.

It's related to conjugation rather than plurality in this case. In this sentence "Jaké barvy" is singular genitive case. Singular nominative would be "Jaká barva" and plural nominative (as well as plural accusative) in this case would be same as singular genitive: "Jaké barvy" ;-)