We present a systematic investigation of phonon-mediated superconductivity across a broad set of kagome-derived intermetallic compounds spanning multiple binary and ternary structural families. Candidate materials were screened for thermodynamic (meta-) stability within 30~meV/atom of the convex hull and for dynamical stability using density-functional perturbation theory phonon calculations. For dynamically stable systems, electron--phonon coupling and superconducting transition temperatures were evaluated within the Allen--Dynes/Eliashberg framework. The first-principles analysis covers the families \ce{AB} (CoSn-type), \ce{AB5} (CaPt$_5$-type), \ce{AB3} (Ni$_3$Sn-type and Pd$_3$Zr-type), \ce{A3B5} (Ba$_3$Al$_5$-type), and \ce{AB2C3} (CsS$_2$Au$_3$-type), together comprising more than a thousand (meta-)stable kagome compounds.

Across these systems, the electronic structures consistently exhibit kagome-related features, including Dirac-like crossings, weakly dispersive bands, flat-band manifolds, and Van Hove singularities, whose energetic positions vary substantially with chemical composition. The calculated superconducting properties span broad ranges depending on the structural family, with electron--phonon coupling constants reaching $\lambda\!\sim\!2.5$ and transition temperatures up to approximately 12~K.

To explore larger compositional spaces, superconducting properties of the \ce{AB2C9} (\ce{BaCo2Al9}-type) and \ce{A2B3C7} (\ce{Ag2Ca3Al7}-type) families were predicted using a machine-learning model trained on the first-principles dataset. The predicted ranges are $\lambda^{\mathrm{ML}}=0.07$--1.84 and $T_c^{\mathrm{ML}}$ up to 11.67~K for the \ce{AB2C9} family, and $\lambda^{\mathrm{ML}}=0.09$--1.06 with $T_c^{\mathrm{ML}}$ up to 11.08~K for the \ce{A2B3C7} family.

The combined first-principles and machine-learning results provide a unified dataset of stability, lattice dynamics, electron--phonon coupling, and superconducting transition temperatures across multiple kagome structural families.