ANSWER:
For whatever reason, it appears the -ms-flex line must be set to 1 0 auto; instead of just 1. So the corrected CSS would look like:
.content {
display: block;
flex-direction: row;
height: 100%;
}
.contentFieldset {
flex: 1;
-ms-flex: 1 0 auto;
min-width: 0;
display: block;
flex-direction: column;
}
.inner {
display: block;
flex-direction: row !important;
flex: 1;
-ms-flex: 1 0 auto;
min-width: 0;
}
I'm not sure why this works, but I suspect the default for -ms-flex is processed differently then flex in IE.