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.

The DHS Wealth Index is relative with a mean of zero and a standard deviation of 1.0. Thus it is different from an absolute measure of wealth in that a household with no net worth would have zero wealth. Net worth cannot be determined with a DHS (or maybe any other survey), since it involves assigning monetary values to everything owned and subtracting every owed. Many household may owe more than they own, and in that case their net worth is negative.

The DHS wealth index has two forms of data: the wealth index score assigned to each household and the wealth index quintile, derived from the wealth index score, to which a household is assigned. The wealth index score is an interval rather than a ratio scale since the zero point does not mean zero wealth. A concentration index, Gini coefficient and Lorenz curve can be calculated from the wealth index score. To calculate them, add a constant to each score that is the value of the lowest score with its sign changed such that the lowest score would then be zero. To measure changes in inequality over time or across countries, first apply the comparative wealth index transformations to the scores for each survey.

However, the wealth index does not handle extremely wealthy households well as the data on number of possessions and their values are not obtained by the DHS, and may thus underestimate wealth inequality for all households in the country. That is, the most wealthy households may appear to have the same scores as the next most wealthy households. To estimate these

For the inequality calculations, cardinality does not enter in since the number of members of the group is the number of households interviewed and the interval scale can theoretically have an infinite number of values.

The wealth index score can be used directly to calculate the concentration index. There is no need to recalculate by region since it is nationally comparable for a given survey.