Nested column flexbox inside row flexbox with wrapping

I've been playing with this for a few minutes now, and I think I've got what you're looking for.

Here's the CSS

.flex-group {
    margin: auto;
    display: flex;
    flex-direction: row;
    justify-content: space-around;
}

.flex-container {
    flex: 0 1 auto;

    display: flex;
    flex-flow: row wrap;
    align-items: space-around;
    align-content: flex-start;

    padding: 0;
    margin: 0;
    list-style: none;
    border: 1px solid silver;
}

.red li {
    background: red;
}

.gold li {
    background: gold;
}

.blue li {
    background: deepskyblue;
}

.flex-item {
    flex: 0 1 auto;

    padding: 5px;
    width: 100px;
    height: 100px;
    margin: 10px;

    line-height: 100px;
    color: white;
    font-weight: bold;
    font-size: 2em;
    text-align: center;
}

And here's an updated fiddle to see it in action.