High-throughput synthesis and screening of chemical libraries play pivotal roles in drug discovery. Click chemistry has emerged as a powerful strategy for constructing highly modular chemical libraries. However, the development of new click reactions and unlocking new clickable building blocks remain exceedingly challenging. Herein, we describe a double-click strategy that enables the sequential ligations of widely available carboxylic acids and amines with fluorosulfuryl isocyanate (FSONCO) via a modular amidation/SuFEx (sulfur-fluoride exchange) process. This method provides facile access to chemical libraries of N-fluorosulfonyl amides (RCONHSOF) and N-acylsulfamides (RCONHSONR'R'') in near-quantitative yields under simple and practical conditions. The robustness and efficiency of this double click strategy is showcased by the facile construction of chemical libraries in 96-well microtiter plates from a large number of carboxylic acids and amines. Preliminary biological activity screening reveals that some compounds exhibit high antimicrobial activities against Gram-positive bacterium S. aureus and drug-resistant MRSA (MIC up to 6.25 μg ⋅ mL). These results provide compelling evidence for the potential application of modular click chemistry library as an enabling technology in high-throughput medicinal chemistry.