I just read the article and while at least of the anti-frizz products listed contains silicones, the advice regarding gel said to use a "silicone and alcohol free gel," which I take to mean both silicone-free and alcohol-free.

3a/f/iii
Modified CG since 11/5/11
CLEANSE: VO5 Vanilla Mint Tea Clarifying, DevaCare No-Poo, CHS Treatment Shampoo
RO: DevaCare One Condition, SS Caitlin's Conditioner, Mop Top Daily Conditioner
LI: SS Repairing Protein Treatment, CHS Silk Leave-In
STYLE: Re:Coil, Curl Keeper, Deva Ultra Defining Gel, Curls Rock Amplifier and Strong Hold Mousse, Sweet Curls Elixirs Okra Gel and Hard Hold Gel, SS Curl Enhancing Jelly and Firm Hold Gel