The objective of this article is to introduce valid and robust methods for the analysis of rare variants for family-based exome chips, whole-exome sequencing or whole-genome sequencing data. Family-based designs provide unique opportunities to detect genetic variants that complement studies of unrelated individuals. Currently, limited methods and software tools have been developed to assist family-based association studies with rare variants, especially for analyzing binary traits. In this article, we address this gap by extending existing burden and kernel-based gene set association tests for population data to related samples, with a particular emphasis on binary phenotypes. The proposed approach blends the strengths of kernel machine methods and generalized estimating equations. Importantly, the efficient generalized kernel score test can be applied as a mega-analysis framework to combine studies with different designs. We illustrate the application of the proposed method using data from an exome sequencing study of autism. Methods discussed in this article are implemented in an R package gskat, which is available on CRAN and GitHub.