dna - How can you identify if a person is homozygous for a certain allele?

You could use a 3-primers strategy, where you have a common primer, one that only amplifies the mutant allele and one that only amplifies the wt. This may or may not be feasable depending on the type of mutation.
DNA from het people will amplify both product, while homozygous will only amplify one (wt or mutant).

Of course then, linking the mutation of a gene to the lack of a chemokine is not necessarily straightforward.

To be honest, however, I would use a different approach: take people who don't produce the chemokine, and people who do (simply by dosing the chemokine in the blood). Now sequence the gene in the two groups and look for mutations.