My experience of activating Handy Internet Flatrate on a new SIM:
Sent 'START HANDYINTERNET', was asked for confimation, sent 'JA', and got an SMS that it would be activated soon : 'Sie erhalten in Kuerze...'. Nothing for 3 days. I tried using the AP 'Internet, but still on volume-based charging.
So yesterday I went on the Mein Fonic site
https://www.fonic.de/selfcare2/servlet/Start
and changed the data tariff there - very easy. I got an SMS to say it was activated today, 18 hours later, and the balance has been debited.