Could sodium fluoride or aluminum accumulation in soils contribute to increased amounts of palmitic acid in food?
This article explains the effects of fluoride ion concentrations to Prosopis juliflora.


  Both catalase (3.2 folds) and peroxidase (2.7 folds) enzymes activity increased with increase in F concentration.


Checking out Wikipedia articles about these enzymes, neither catalase not peroxidase are involved in the fatty acid biosynthesis. So as far as I know, I don't think there's any effect of fluorides in the biosynthesis of palmitic acid.

Also, regarding aluminum ions, this article explains aluminum toxicity as a hindrance to cell division and elongation, but nothing is mentioned about fatty acid synthesis.

References:

Saini, P, et al. “Effects of Fluoride on Germination, Early Growth and Antioxidant Enzyme Activities of Legume Plant Species Prosopis Juliflora.” Journal of Environmental Biology., U.S. National Library of Medicine, 34 Mar. 2013, www.ncbi.nlm.nih.gov/pubmed/24620580.

Mossor-Pietraszewska, T. (2017). Effect of aluminium on plant growth and metabolism.. [online] Psjd.icm.edu.pl. Available at: http://psjd.icm.edu.pl/psjd/element/bwmeta1.element.bwnjournal-article-abpv48i3p673kz [Accessed 23 Aug. 2017].