In this work we study string kernel methods for sequence analysis and focus on the problem of species-level identification based on short DNA fragments known as barcodes. We introduce efficient sorting-based algorithms for exact string k-mer kernels and then describe a divide-and-conquer technique for kernels with mismatches. Our algorithms for mismatch kernel matrix computations improve currently known time bounds for these computations. We then consider the mismatch kernel problem with feature selection, and present efficient algorithms for it. Our experimental results show that, for string kernels with mismatches, kernel matrices can be computed 100-200 times faster than traditional approaches. Kernel vector evaluations on new sequences show similar computational improvements. On several DNA barcode datasets, k-mer string kernels considerably improve identification accuracy compared to prior results. String kernels with feature selection demonstrate competitive performance with substantially fewer computations.