The identification of differentially expressed genes (DEGs) from transcriptomic datasets is a major avenue of research across diverse disciplines. Current bioinformatic tools support a number of experimental designs including covariates, random effects, and blocking. However, covariance matrices are not yet among the features available. Here, we introduce kimma for kinship in mixed model analysis, an open-source R package that provides linear and linear mixed effects modeling of RNA-seq data including all previous designs plus covariance random effects. In unpaired study designs, kimma detects simulated DEGs with similar specificity and sensitivity to limma. In paired designs, kimma has simulated DEG detection equivalent to dream, both of which out-perform limma. Using a multi-processor architecture, kimma achieves run times similar to or faster than the other best-performing software (limma, dream) and can incorporate fit metrics, gene-level weights, co-variates, and interaction terms at no time cost. Using real-world data, kimma has slightly higher sensitivity and detects more DEGs in paired study designs. Finally, we utilize genetic kinship as an example covariance data set and find that kinship impacts model fit among related subjects with consequences for DEG detection in paired designs. Thus, kimma equals or outcompetes other DEG pipelines in terms of sensitivity, computational time, and model complexity.