。
There's something aristocratic about their getup, somehow.
Literal
Outfit [subject-が] somehow aristocrat-[ish-っぽい] [like-ような] feeling [subject-が] do.
A casual observation about someone's appearance. 出で立ち ('outfit, attire, bearing') is a slightly literary/old-fashioned noun. ~っぽい ('-ish, -like') is a productive casual suffix attaching to nouns and adjective stems — 子供っぽい ('childish'), 男っぽい ('manly'). 気がする ('to have the feeling that X, to feel that X') is a fixed expression for subjective impressions. The stacking ~っぽいような is redundant for emphasis — 'a kind of -ish feeling.'