It seems like a daunting task, unless you're specifically parsing a .css file with the intention of incorporating it:
The values in CSS can only be determined by examining the .html file generated from the .Rmd file, but when the R code is executed, the .html file hasn't been created yet.
One approach to make an educated guess on the value is to have your R code generate an .html file from the same .Rmd file you are currently using (being cautious that the nested .Rmd doesn't trigger another rendering process, causing an infinite loop). Then analyze that .html file to determine the current value of the variable within the code chunk seeking that information.