It doesn’t sound particularly difficult. But making ones that end up sounding good might be more of a challenge. First up, you’d need a randomizer. There are probably many of them around. I have one that gives a repeatable sequence, based on a seed value, starting by default with a timestamp, but re-seedable as necessary, and I’m sure there are many other similar implementations. Mine is in my Bullshit Bingo wiki.
You’ll need a list of words to use. You can maintain a single tiddler with a list of words and parse out start letters as you go, or, my preference, keep one tiddler per letter. If you’re looking for random words, I’ve been happy with some of the other tools at Random Adjective Generator — Generate 1000+ Random Adjectives.
You might want to get a little more sophisticated and maintain separate lists of adjectives and nouns, as the last word should probably be a noun. But that’s an implementation detail.
Sorry, the above was based on a too-quick reading of the problem. (Of course, I like that problem more than the original! )