Thanks for the interest in AT and hopefully it will be a core feature that a lot of other very useful things can be built on top of.
As AT cannot keep secrets I think a very simple version of what you are wanting is not really going to be possible, however, I can think of one approach that might make it very hard for anyone to "follow the funds" and that is to make a variation of the current "atomic cross-chain transfer" use case (
http://ciyam.org/at/at_atomic.html) in which the hash published in the initial AT is not the same as what is used in the other AT (which is created on another blockchain).
The idea would be that the second AT would have a hash that is a function of the first hash (rather than just the secret itself - you'd therefore have to calculate the relevant hash to feed the second AT offline). Although when there are very few ATs in existence it would still be easy to track the funds when there are thousands or more of such ATs it would become very hard to work out which transaction matches which (thus starting to approach the plausible deny-ability of CoinJoin assuming the function you used is sufficiently complex enough to not be discovered).
Very interesting, thanks for the insight. And congrats on nearing completion of getting ATs integrated into Burstcoin!
I like the idea of using the cross-chain transfers mechanism to trade funds between accounts in a way that is nearly unlinkable. It seems like this could even be used to trade unequal amounts, by incorporating randomness into the ATs (users that did this would have to accept a risk that they may lose coins for a given trade, but they should break even in the long run). This would help solve one of the major problems of CoinJoin - that you need to find people that want to trade the exact same amount of coins as you. The only major downside though, is that it still seems to need some sort of other channel of communication in order to communicate the secret function between the 2 parties.
It would be awesome if it were possible to create a lottery AT that uses some sort of zero-knowledge algorithm to choose a winner. The winner could claim their winnings by sending a message to the AT that proves they are the winner without revealing which account they originally sent the coins from. I feel like this should be possible, given that ATs are Turing complete, but I don't have an in-depth enough understanding to really say for sure.