Spin-1 kagome lattice antiferromagnets provide a versatile platform for exploring exotic quantum states, such as classical spin liquids and spin nematics, owing to the confluence of geometric frustration, bilinear and biquadratic interactions, and single-ion anisotropy. Here, we investigate the ground state and spin dynamics of a nearly perfect s = 1 kagome lattice, \({({\text{CH}}_{3}{\text{NH}}_{3})}_{2}{\text{NaV}}_{3}{\text{F}}_{12}\), which hosts dominant antiferromagnetic interactions (J ≈ 10 K) alongside easy-axis anisotropy. Using a combination of thermodynamic and resonance techniques, we identify the occurrence of weak ferromagnetic ordering at TC ≈ 4 K. Singularly, even in this time-reversal symmetry-breaking state, muon spin relaxation, 23Na spin-lattice relaxation rate, and magnetic specific heat measurements collectively reveal persistent spin dynamics and intriguing gapless excitations. The observation of liquid-like correlations in the ground state establishes \({({\text{CH}}_{3}{\text{NH}}_{3})}_{2}{\text{NaV}}_{3}{\text{F}}_{12}\) as a rare instance of the coexistence of dynamically fluctuating spins and weak ferromagnetism, raising the possibility of realizing an intriguing ground state in s = 1 kagome antiferromagnets with Ising anisotropy.