Best practice to perform a functional analysis on a set of VCFs from a cohort of patients
As a simple approach you may want to try the "fuzzy" list implemented in EnrichR itself. There is some information about this in the Help Center under the "What is a gene set" heading.   

This way you can code the number of data sets a gene appears as a value between 0 and 1. In the Help Center this is used to convert fold changes or p-values to a membership score but I don't see why this would not also work for the number of data sets a SNP is observed in.  

Since it is relatively easy to implement this can give you an first impression of what to expect. It then may be combined with analyzing each data set independently and then comparing the overlap.