I basically have this figured out, didn't see your comment until after.
The first hint was when Fs popped up in the first digit, which would make the color pretty red, so I thought F might mean "red". Red is the last color on the color spectrum and it was the highest letter that ever appeared.
So my first hypotheses was that every successive digit modified the previous digit, adding an amount of a certain color. But that didn't make sense because I knew FFFFFF was white. If my hypotheses were true, then it would be red.
I realized right there that I'm adding at least three different colors together. How did I realize this? You add colors to make white. From there I was looking at splitting the hex color into different pieces, and if each piece is at its highest intensity then you will have white (FFFFFF). F being the "highest" influencer of a color. I knew the first to be red.
I clicked a bunch, taking note of where the Fs popped up and the color. I was thrown off by second "digit" Fs. After figuring out which digits didn't influence the color much, I basically had it.
It wasn't hard to figure out. I'd like to know how long it takes someone who doesn't know that hex is sixteen.
Note: This really only took me about ten minutes.