In Case someone is trying this not on body but some child div.
You can just set height: 0; on the element with the min-height.
IE just wants any height on the parent element of the flex-grow auto element.
So it could look like this:
.flex-parent{
display: flex;
min-height: 300px;
height: 0;
}
.flex-child{
flex: 1 1 auto;
}