Advances in high-throughput technologies have originated an ever-increasing availability of omics datasets. The integration of multiple heterogeneous data sources is currently an issue for biology and bioinformatics. Multiple kernel learning (MKL) has shown to be a flexible and valid approach to consider the diverse nature of multi-omics inputs, despite being an underused tool in genomic data mining. We provide novel MKL approaches based on different kernel fusion strategies. To learn from the meta-kernel of input kernels, we adapted unsupervised integration algorithms for supervised tasks with support vector machines. We also tested deep learning architectures for kernel fusion and classification. The results show that MKL-based models can outperform more complex, state-of-the-art, supervised multi-omics integrative approaches. Multiple kernel learning offers a natural framework for predictive models in multi-omics data. It proved to provide a fast and reliable solution that can compete with and outperform more complex architectures. Our results offer a direction for bio-data mining research, biomarker discovery and further development of methods for heterogeneous data integration.