You will never get Clay to run through a sluice. As russau pointed out I'm sticky and hide my gold well. If you do find me in your sluice I will rob all your gold and leave you with some nasty waste water.
Better to stay with sand and gravel. You will live longer and I won't be nearly as cranky after your attempts to "break me up".
Heavy Pans
p.s. The very fine particles that form clay are attracted to one another due to their natural electrical potential (charge). The proper application of chemistry can break those charge bonds and dissolve the clay into ordinary muddy water. Change up your pH in the right direction with enough water and your clay will liquefy much better.
p.p.s. It's a rare circumstance when the value of the gold content justifies the expenditure on chemicals to break up the clay.
p.p.p.s. If you still want to try experimenting with chemistry to break down clay - sodium carbonate, soda ash or washing soda (all the same chemical) is a good cheap safe place to start.