May I venture to suggest that that "loud checks' has to be imagined in the context of the OP's late 19th century (1899) and the milieu of Raffles. This more than likely refers to a 2-piece (jacket & trousers/pants) or 3-piece suit (jacket, trousers/pants & waistcoat/vest) made from cloth with a bold check-pattern. The landed gentry would wear this kind of attire in London on a Friday, just prior to departing for a weekend in the country where, in season, they would enjoy a few days of field sports, changing into hunting pinks, Plus Fours and the like.
A suit with a very loud check-pattern was something of a "statement" when worn by urban bounders and cads of the day. The pattern was more likely to be at the far end of the loud spectrum. The OP's context would suggest an urban bounder in a very loud check suit rather than a bespoke Savile Row suit as worn by a toff.
EDIT: See GRENVILLE, Richard Plantagenet, Duke Buckingham depicted loud check