The problem is that percentage-based widths are based off of the immediate parent. If the immediate parent has no width, the child cannot know what 100% of an arbitrary value is. flex: 1 is shorthand that contains flex-grow: 1, meaning that #flex2 can grow infinitly without setting this width constraint.
Percentage-based widths bubble up to the point a fixed width is known, so all you have to do is set a width of 100% of #flexchild2 as well in order for #flexchild3 to inherit the width of #flexparent:
This can be seen in the following:
#flexparent {
display: flex;
}
#flexchild1 {
flex: 1;
background-color: green;
}
#flexchild2 {
flex: 1;
background-color: red;
display: flex;
flex-flow: column;
width: 100%;
}
#flexchild3 {
background-color: purple;
width: 100%;
word-wrap: break-word;
}
<div id="flexparent">
<div id="flexchild1">
FLEXCHILD1
</div>
<div id="flexchild2">
FLEXCHILD2
<div id="flexchild3">
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</div>
</div>
</div>
However, note that due to you using two columns, you'll probably want to give #flexparent a width of 100%, and set your two columns to 20% and 80% respectively. Note that #flexchild3 still inherits 100% of the width of #flexchild2 (which is 80% of the width of #flexparent):
#flexparent {
display: flex;
width: 100%;
}
#flexchild1 {
flex: 1;
background-color: green;
width: 20%;
}
#flexchild2 {
flex: 1;
background-color: red;
display: flex;
flex-flow: column;
width: 80%;
}
#flexchild3 {
background-color: purple;
width: 100%;
word-wrap: break-word;
}
<div id="flexparent">
<div id="flexchild1">
FLEXCHILD1
</div>
<div id="flexchild2">
FLEXCHILD2
<div id="flexchild3">
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</div>
</div>
</div>
Hope this helps! :)