I'm glad you are using tRophicPosition.
Technically, you can't compare two different tissues, because if you have differences between locations or species, you will never know how much is due to differences in tissues or due to intrinsic differences between locations or species. Having said that, you still can compare the trophic position, but I suggest that first you convert fin clips isotope values to muscle isotope values and whole body isotope values to muscle isotope values, then calculate trophic position. If you don't know how those tissues relate each other, then I'm afraid that the pairwise comparisons might be skewed.
pairwiseComparisons() will always work as long as you pass it a list. See this example:
a <- rnorm(100, 2, 0.1)
b <- rnorm(100, 1.8, 0.1)
c <- rnorm(100, 2.2, 0.1)
pairwiseComparisons(list("a" = a, "b" = b, "c" = c))
Here I created a list and used it as argument to pairwiseComparisons. When you use multiSpeciesTP(), you will have a list of 4 elements, in which the third ("TPs") has all the raw posterior trophic position for all species and models, thus you can us it directly as an argument to multiSpeciesTP().
When you use posteriorTP(), as you noted, you have a mcmc object, that depending on how many chains you run, you will have to tweak it a little bit. For example, if you saved in "samples" the results of your model as returned by posteriorTP() use
combined <- coda::mcmc(do.call(rbind, samples))
to combine the different chains of your mcmc object. You should do this for every species/tissue/site, then combine each combined result into a list and use it in pairwiseComparisons.
Please let me know if it works.