Research on human microbiome has suggested associations with human health, opening opportunities to predict health outcomes using microbiome. Studies have also suggested that diverse forms of taxa such as rare taxa that are evolutionally related and abundant taxa that are evolutionally unrelated could be associated with or predictive of a health outcome. Although prediction models were developed for microbiome data, no prediction models currently exist that use multiple forms of microbiome-outcome associations. We developed MK-BMC, a Multi-Kernel framework with Boosted distance Metrics for Classification using microbiome data. We propose to first boost widely used distance metrics for microbiome data using taxon-level association signal strengths to up-weight taxa that are potentially associated with an outcome of interest. We then propose a multi-kernel prediction model with one kernel capturing one form of association between taxa and the outcome, where a kernel measures similarities of microbiome compositions between pairs of samples being transformed from a proposed boosted distance metric. We demonstrated superior prediction performance of (i) boosted distance metrics for microbiome data over original ones and (ii) MK-BMC over competing methods through extensive simulations. We applied MK-BMC to predict thyroid, obesity, and inflammatory bowel disease status using gut microbiome data from the American Gut Project and observed much-improved prediction performance over that of competing methods. The learned kernel weights help us understand contributions of individual microbiome signal forms nicely. Source code together with a sample input dataset is available at https://github.com/HXu06/MK-BMC.