I have found that bark peelings have worked great for me this year. I don’t have clay soil here but it does still get slippy in wet weather. I think that a coarser material like bark chippings could do very well for you, though it wouldn’t last long in the event of flooding I wouldn’t think.
We once bought hardcore from a builders merchants for a path. It consists of what I can only assume is some type of stone, every size from coarse sand size, to an inch or slightly more, in a pale grey colour. When you put it down all of the stone pieces combine and mesh together, between your raised beds I would think that hardcore would work if it is well pressed together. But it is heavy to move around and not cheap, plus you would need to have access for a lorry presumably, to deliver it.
Sorry that I can’t be of more help.