Heat is carried by different types quasiparticles in crystals, including phonons, charge carriers, and magnetic excitations. In most materials, thermal transport can be understood as the flow of phonons and charge carriers; magnetic heat flow is less well-studied and less well understood. Recently, the concept of the flat band, with a vanishing dispersion, has gained importance. Especially in electronic systems, many theories and experiments have proven that some structures such as kagome or honeycomb lattices hosts such flat bands with non-trivial topology. Even though a number of theories suggest that such dispersionless mode exist in magnonic bands under the framework of the Heisenberg spin model, few experiments indicate its existence. Not limited to these flat band effects, magnetic insulators can assume a variety of nontrivial topologies such as magnetic skyrmions. In this thesis, I investigate the highly frustrated magnetic system Y0.5Ca0.5BaCo4O7, where the kagome lattice could potentially lead to nontrivial thermal transport originated from its flat band. While we do not observe signatures of the flat band in thermal conductivity, the observed anomalous Hall effect in electrical transport and spin glass-like behavior suggest a complex magnetization-transport mechanism. Motivated by the rapid advancement of artificial inteligence, the application of machine learning into materials exploration is recently investigated. Using a graphical representation of crystallines orginally suggested in Crystal Graphical Convolutional Neural Network (CGCNN), we developed the ML-asssited method to explore magnetic compounds. Our machine learning model can, so far, distiguish ferromagnet or antiferromagnet systems with over 70% accuracy based only on structual/elemental information. Prospects of studying more complex magnets are described.S.M.