I apologize in advance if anything I say you already know. FL is a very deep program with a lot of hidden stuff. I know a lot of people ignore it (I didn't even look until I had basically mastered it), but the manual/documentation is actually really, really good and well-written. I'm also using FL11, but I doubt any of this stuff has changed between the two.
1. Make sure you're working in the playlist (F6) and not the step sequencer (F5). Step sequencer/piano roll(F7) makes patterns, playlist uses patterns and audio clips to make your song. The automation clips go there alongside the patterns.
2. Right click the mixer knob to the right of the effect in your Insert channel. (Side note: Pretty much everything throughout the program has right click functionality - you will be very surprised at what can do what, and what can be linked together. Right click everything.)
3. Click 'Create Automation Clip' in the menu that pops up. This is just one way to do this. There's also 'Edit events,' which directly sets values over the course of the entire song - they have different functionality, I'm not well-versed in why they exist other than for note parameters in the piano roll.
You can also click 'Link to controller' to link other knobs to the same curve, or to special controller effects like Peak Controllers (these track volume going through them, and contain a built-in LFO), Formula Controllers, and the Keyboard Controller if you have a MIDI device.
4. In your playlist, you should have gotten an automation clip for the effect. Should look something like this to begin with:
It always starts out with two points at either end of the song set to what value the knob originally was at, and runs the entire current length of the song. Inside the clip are points of a line. You add them by right clicking anywhere within the automation clip, and the value of the knob tracks the line of the curve. When you right click a point after adding it, you get this menu:
You should experiment with all of them, but if you just want to set it to a specific value at a specific time, you want Hold.
The points can be dragged around, and right clicked to paste in values you get by right clicking other things and using 'copy value' (or by running calculator shenanigans if you want to get fancy). The clip can also be moved and resized to the right, and you can duplicate multiple automation curves over the course of a track to do the dubsteps. If you delete an automation clip, you can readd it the same way you do a pattern - at the top where it lists 'Playlist - Fruity Free Filter (Insert 1) - Mix level' is a dropdown that gives you access to every pattern, clip, and audio sample in the project.
And at the top left corner of the clip itself, in the menu that drops down on left click, the "channel settings" option gives you a built-in LFO with tension, skew, pulse-width, level, speed, and min/max control if you want your effect to move in waves. Little known/useless fact: Ridiculously, all of these can be automated as well, so you can automate your automation curves with more automation curves if you want to get that kind of meta.
Let me know if anything's unclear or if you have more questions
You're also welcome to bounce questions off of me on Skype - genericskypenamewiththehat