For biointegrated flexible systems that acquire and process electrophysiological signals, amplifying weak biosignals from their original low amplitudes (ranging from microvolt to millivolt) to volt-level is essential for subsequent processing. Achieving this level of amplification requires a high voltage gain (>105 or 100 decibels for microvolt signals). However, realizing such gain in flexible circuits remains highly challenging because of constrained integration scale and limits in feasible circuit topologies. Here, we report flexible amplifiers that achieve ultrahigh gain by leveraging intrinsic gain singularities induced by negative differential resistance (NDR) effect in carbon nanotube-based transistors. The NDR behavior is investigated under various factors, including contacts, gate structures, and channel lengths. Guided by insights into the correlations between NDR characteristics and device-level parameters, a device-circuit codesign approach is implemented to build a flexible amplifier achieving a record-high gain of 104 decibels among all reported flexible amplifiers, with successful demonstration of electroencephalogram signals amplification.