In order to achieve high-quality 3D printing of inorganic materials, a thorough evaluation of appropriate rheological characteristics and methodologies for formulating all-inorganic inks is required. We recently reported all-inorganic inks using BiSbTe-based thermoelectric particles coupled with a chalcogenidometallate (ChaM) inorganic binder. In the current study, we analyzed the rheological behavior of the all-inorganic inks to assess printability and 3D structural retention with respect to the ChaM content. The stress sweep and three-interval thixotropy test (3ITT) were conducted to mimic a 3D printing and interpret the flow behavior under nonlinear viscoelastic region. The binder-free inks showed a sharp overshoot of the loss modulus (G″) followed by the fluctuation of both the storage modulus G′ and G″ in the stress range of 10-50 Pa. In addition, the inks developed stronger colloidal structure than the initial state after the 3ITT, resulting in the non-uniform jetting. The nonlinear flow of the inks became stable by incorporating ChaM. However, the excessive ChaM (37.5 wt. %) brought about stress-induced structure regeneration analogous to the binder-free inks. The 3D structure integrity was interpreted by yield stress and solid-like characteristics based on the frequency sweep results after undergoing deformation. Poor printability from the 12.5 wt. % ChaM-containing ink was correlated to low yield stress (2 Pa) and a high slope of the G′ curve. However, the 25 wt. % ChaM-containing ink gave a high yield stress of 48 Pa and a low G′ curve slope of 0.2 even after nonlinear deformation, resulting in high 3D shape retention and printability.