If you've seen this pattern then you'll probably remember it - the juggler's arms cross and uncross, and the balls or clubs follow each other one way and then the other. If you can do Mills Mess with three balls then it's pretty much the same with clubs.
Just a quick note about the name: I've heard this pattern called many things, some of the better ones include Bill's Mess, The Miller's Mess and The Mish-Mash. It's definitely "Mills" as in Steve Mills and it's definitely "Mess", as in ... mess.
Assuming that you have learnt the pattern with balls, the following hints may help for clubs:
Hold the clubs near to the end of the handle, this way your hands don't have to move as far to make all the under arm throws; for the same reason use your wrists rather than your arms when throwing.
Angling the clubs away from the throw can give you a bit more space within the pattern, i.e. if you are throwing the clubs to the left, point the body of the club slightly to the right and vice versa. Doing this makes the trick look nicer, but the catches can be a little more awkward.
When juggling balls, the most common way to transition into Mills Mess is from a reverse cascade, however I find this to be a rather awkward trick with clubs. My preferred method is simply an underarm throw from a cascade, or an Elbow Roll.
To enhance the pattern, once you have it under control, experiment with some vertical floaters - they look very effective if done nicely.
There are dozens of Mills Mess variations, such as The Half Mess, Reverse Mess, Fake Mess, Inverted Mess and Burke's Barrage to name but a few - these tricks will all transfer very nicely from balls to clubs. As with Mills Mess, if you can do them with one then you can probably do them with the other, and I don't intend to describe them all here. I would refer anyone wishing to explore this area to George Gillson's highly detailed book Beyond the Cascade.