Severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) continues to threaten lives by evolving into new variants with greater transmissibility. Although lateral flow assays (LFAs) are widely used to self-test for coronavirus disease 2019 (COVID-19), these tests suffer from low sensitivity leading to a high rate of false negative results. In this work, a multiplexed lateral flow assay is reported for the detection of SARS-CoV-2 and influenza A and B viruses in human saliva with a built-in chemical amplification of the colorimetric signal for enhanced sensitivity. To automate the amplification process, the paper-based device is integrated with an imprinted flow controller, which coordinates the routing of different reagents and ensures their sequential and timely delivery to run an optimal amplification reaction. Using the assay, SARS-CoV-2 and influenza A and B viruses can be detected with ≈25x higher sensitivity than commercial LFAs, and the device can detect SARS-CoV-2-positive patient saliva samples missed by commercial LFAs. The technology provides an effective and practical solution to enhance the performance of conventional LFAs and will enable sensitive self-testing to prevent virus transmission and future outbreaks of new variants.