I don't think any of Richard's direct ancestors died of the plague, but poor little Princess Joan, daughter of Edward III (and sister of three of the York sons' ancestors) contracted the Black Death in 1348 on her way to the Continent to marry Pedro of Castile (whose reputation seems as divided as Richard's is). She was only fourteen when she died.
And, of course, Henry Tudor's father, Edmund, Earl of Richmond, died of the plague in 1456, but that may have been a different disease.
I could be overlooking someone, of course. I don't know much about the Mortimers (except that Anne Mortimer, the Duke of York's mother, died in childbirth or soon after). Maybe one or more of the male Mortimers died of the plague/Black Death?