I’ve just read about something called ankle jerk. Apparently, if I stretch the Achilles tendon of my foot tight by flexing it at the ankle and then tap my Achilles tendon, I should experience a reflex contraction of my calf muscles.

I just tried it on my foot – but didn’t experience any involuntary muscle twitching!

Is this abnormal? Or am I doing the ankle-jerk experiment correctly?

It's probably because you're doing it to yourself. Bending over weirdly to reach your foot, perhaps tapping with your fingers instead of the suggested rubber hammer, your ankle might not be in the correct position. Lots of things that can go wrong. I wouldn't worry too much about any major medical malfunction in your feet.