In this article, we examine the propagation of small-amplitude dust ion-acoustic (DIA) solitary waves in an unmagnetized three-component dusty plasma composed of negatively charged mobile dust, ions, and electrons obeying the Kaniadakis distribution. By applying the standard reductive perturbation method, the Korteweg–de Vries (KdV) and the modified KdV (mKdV) equations are derived to explore the effects of key plasma parameters, viz., the Kaniadakis deformation parameter (κ), the dust charge number (Z_d), and the initial streaming speed of ions (u_i0) and dusts (u_d0), on the evolution of DIA solitary waves. A wide range of notable features emerges, showing how the solitary profiles respond to variations in key plasma parameters. The analysis reveals that for certain values of initial ion streaming speed and dust charge number, a non-existence region of KdV-DIA solitons arises. Both compressive and rarefactive KdV-DIA solitons and only compressive mKdV-DIA solitons are observed under the same plasma conditions. For compressive structures, the soliton amplitude increases with increasing Z_d and decreasing κ. The results further demonstrate that the Kaniadakis deformation parameter (κ) significantly modifies the properties of mKdV-DIA solitons, while it does not influence the characteristics of KdV-DIA solitons. In addition, the dependence of the width of DIA solitons on various plasma parameters is also investigated.