High-quality III-V narrow band gap semiconductor materials with strong spin-orbit coupling and large Landé g-factor provide a promising platform for next-generation applications in the field of high-speed electronics, spintronics, and quantum computing. Indium Antimonide (InSb) offers a narrow band gap, high carrier mobility, and a small effective mass, and thus is very appealing in this context. In fact, this material has attracted tremendous attention in recent years for the implementation of topological superconducting states supporting Majorana zero modes. However, highquality heteroepitaxial two-dimensional (2D) InSb layers are very difficult to realize owing to the large lattice mismatch with all commonly available semiconductor substrates. An alternative pathway is the growth of free-standing single-crystalline 2D InSb nanostructures, the so-called nanoflags. Here we demonstrate fabrication of ballistic Josephson-junction devices based on InSb nanoflags with Ti/Nb contacts that show gate-tunable proximity-induced supercurrent up to 50 nA at 250 mK and a sizable excess current. The devices show clear signatures of subharmonic gap structures, indicating phase-coherent transport in the junction and a high transparency of the interfaces. This places InSb nanoflags in the spotlight as a versatile and convenient 2D platform for advanced quantum technologies.