According to Official Guinness Records,
The most silver medals awarded in a single Olympic swimming race is three by Michael Phelps (USA), Chad le Clos (South Africa) and László Cseh (Hungary), who all tied second in the Men’s 100 m butterfly, at the 2016 Olympic Games held in Rio de Janeiro, Brazil, on 12 August 2016. All three swimmers recorded a time of 51.14 seconds. This was the first ever three-way tie in an Olympic swimming event.
For a complete list of 2016 records, please visit 2016 Guinness Records in Brazil.