A simple, efficient, and selective oxidation under flow conditions of sulfides into their corresponding sulfoxides and sulfones is reported herein, using as a catalyst perselenic acid generated in situ by the oxidation of selenium (IV) oxide in a diluted aqueous solution of hydrogen peroxide as the final oxidant. The scope of the proposed methodology was investigated using aryl alkyl sulfides, aryl vinyl sulfides, and dialkyl sulfides as substrates, evidencing, in general, a good applicability. The scaled-up synthesis of (methylsulfonyl)benzene was also demonstrated, leading to its gram-scale preparation.