Hi! Sorry for the late response, but this month is going to be crazy for me.
I tried out the first week and I'm fairly happy with how their videos and their explanations of exactly how the drills help you swim better. In addition, the first week focused on "imprinting" body position in the water and the drill definitely clicked for me. (Since I remember the importance of imprinting from TI).
As for kicking, there was a kick portion in the warmup, but I'm sure you can skip that. I believe it says somewhere on the webpage that you should learn correct kick rhythm, whether it's a 2 beat, 4 beat, or 6 beat kick. From what I understand, Total Immersion is almost a 2 beat kick, where you use the kick to generate body torque; however, it is more of an afterthought. The second week of drills for Finding Freestyle look like it's focused on accurate timing of those kicks so you get the most out of the torque. I don't think you need a kickboard for the second week. Hope this helps.