Thank you so much for taking the time to look at this issue Eric.
I looked over the solution on SO and that does indeed solve that issue. I worked through it and I am realising that the SO question is slightly different than mine.
I put together a little example that is displaying the specific issue I was having:
<!doctype html>
<html lang="">
<head>
</head>
<body unresolved fullbleed layout vertical>
<polymer-element name="top-el" noscript>
<template>
<child-el>
<div id='child-content' header>
<span>Hello</span>
<span flex></span>
<span>world</span>
</div>
</child-el>
</template>
</polymer-element>
<polymer-element name="child-el" noscript>
<template>
<core-toolbar>
<content select=[header]></content>
</core-toolbar>
</template>
</polymer-element>
<top-el></top-el>
</body>
</html>
If I use the above example it does not flex as I expected, however, I believe this is user error. In the example above when I set the child-content div to have a style="width:100%" and add the attributes layout and horizontal things work as expected.
<child-el>
<div id='child-content' style='width:100%' header layout horizontal>
<span>Hello</span>
<span flex></span>
<span>world</span>
</div>
</child-el>
I can also seem to get things to work as expected by replacing the child-el with the following:
<child-el>
<span header>Hello</span>
<span header flex></span>
<span header>world</span>
</child-el>
This removes the wrapper div and seem to be the preferred way to handle this situation.
as a note I tried adding fit to the child-content div and it seems to mess up some of the styling that core-toolbar applies.
I think that the problem had to do with the way I was thinking about this problem. I was looking for a way to wrap a set of elements and have them inserted into my content tag. However, I think the method of adding multiple header attributes to the different sections seems to be the correct way to handle this as it gives me a finer level of control over what goes in and how.
I wanted to document my process a bit in case anyone else runs across a problem like this.
Thanks again for your time.