I'm not sure exactly how you want to use the wealth index, but there are definitely measures of inequality you could use depending on the context. Do you want to ask something like how the variance of wealth index affects some other variable? Is the comparison within-regions of some country, or inequality within a country relative to other countries, or...? If you give a little more context I might be able to help better, but here are a few thoughts to get you started:

As to the specific question - the wealth index is a principle component analysis of various characteristics/assets of the household. In the theoretical world where this is latching on to some real, underlying wealth parameter, than I think you can argue they have cardinal properties (within each survey round at least). But I don't think anyone really believes that (whether they believe it "enough" to think it is useful, I'd say depends on the person). In another world where you just think it gives a generally good ranking of households, you could still use it to estimate inequality effects in some round-about kind of way (maybe by using differences in how many people in some area are in the top or bottom quintile or something).

One other possibility is to bring in inequality data from another source and merge it with DHS data - that is, if there is some outcome in the DHS you are interested in that you think might vary by wealth inequality.