Suggestions

[The Unintelligible]

The aforementioned was not rainbow.

You should use HSL to generate the colors, and then just convert it to RGB when outputting as hex.

Hue is beautifully simple. Just scale it by whatever-max-hue-is-i-think-360 divided by the number of characters in the string (minus the number of spaces if you want).

Define a function or procedure that takes as input a string that you will convert to arbitrary "rainbow" BBCode

My algorithm isn't systematic. As in, it doesn't conform to a standard "rainbow" algorithm like what you're describing. I wasn't trying to accomplish that. After some thought, I figured I'd try that one as well but it wasn't my objective.

The criteria I defined was to create something to arbitrarily generate rainbow BBCode. Which by definition is something that consists of its 7 colors.

Artificial's solution was an example of the algorithm you're referring to.