I just made an overly flirtatious joke and when she didn't respond, I knew what it meant. She's usually very flirtatious with everyone, so it was very unexpected behaviour for her.

Smoothly done. Flirtation fulfilling one of its intended roles!

except mutual friends who had been in similar situations with her had tried that, and it made things very awkward between them for a few months

In some situations and for some people I actually consider that a beneficial side effect. It doesn't apply to yourself, of course, but some people lack the self awareness or pragmatic ability to evolve relationships in a beneficial direction based on available information and preferences. In such cases the aversive emotion of awkwardness can prompt a healthy response that they are otherwise too naive to consider. Like 'Next!", for example.