It’s pronounced (not gonna use IPA here) itch-(tiny glottal stop)-tuk-nee.
I’ve heard tourists say:
Itchy-took-nee
Icky-took-a-nee
Icky-tuck-a-nee
Itchy-a-tuck-a-nee
Icky-toke-annie
Ict-toke-nay
Itchy-toch-nay
Icky-tock-nay
And many more I’m sure. When I lived near the confluence of the Santa Fe and Ichetucknee Rivers, every weekend we’d get 1-3 tourists asking where the river was. They never pronounced it right. Not a single time.
Also, nearly none of the YouTube videos or pronunciation guides on the internet render an accurate Ichetucknee pronunciation (as North Florida natives do). All of them totally butcher it. Whoa, I found one woman who gets it about 95% right! She says it as close to a native as anyone I’ve ever heard.
The rest are so bad. But if you ever get a chance, do see the Ichetucknee. It’s one of the most beautiful places in the world.