I have done this before and thought it was easy, but have waisted the last two days getting nowhere. Then, while I was driving home from town my brain screamed Eureka and ran down the road naked.
Change class="flyout" to an ID and put that div inside the socialhover div and we're good to go:
<a href="#">Follow Us</a>
<div id="flyout" class="hidden">
<a href="#">Link 1</a><br>
<a href="#">Link 2</a><br>
<a href="#">Link 3</a><br>
<a href="#">Link 4</a><br>