The scene portraying the young Dash shows her on the back of Rainbow Blaze, who must be her father.
In the same scene, Rainbowshine is shown next to the other two ponies. That would imply she is Dash's mother.
Does Rainbow Dash have any biological siblings? I presume she has no brothers or sisters. That may explain her close friendship to Scootaloo, in which Dash and Scootaloo treat each other almost as if they were real sisters.