I have a dataset where I am interested in looking at differential expression of genes in a singular body fluid and the relationship with a histochemical outcome that is a repeated measure. I would prefer not to collapse this repeated measure into one variable and use it for input into limma due to missing data which would make a composite variable biased.

Therefore, I was wondering whether there was a statistical issue with modeling the genes as independent variables rather than a dependent variable so that my repeated measure could serve as the outcome? That way I could then run a mixed model using dream in the variance partition package or use duplicate correlation in limma?

Sorry, your question doesn't make sense to me. There are tens of thousands of genes and you can't run a mixed model analysis with one dependent variable and tens of thousands of independent variables. That obviously makes no statistical sense. Neither limma or dream are at all applicable for such an analysis.

I am not even clear what you mean by a "repeated measure". You don't seem to be using the term in the same sense as in anova theory. It cannot be true that your outcome variable is repeated but the expression values are not. If you want to relate histochemical outcome to expression, then either both must be repeated or neither.