I think these fatty acids might be a bit tricky to dissolve. Are you already using FBS in the cell culture, and you want to use FBS to avoid other additives? Yes, you can, but there is probably a limited amount that you are able to dissolve. Also remember that there is quite a lot BSA in FBS. Most of the protein in FBS is BSA, corresponding to 3-4 g BSA per 100 ml. You probably have to stirr for quite a while (at elevated temperature, but much higher that 37-40 degrees C may start to affect proteins that could be important for your cells). You may also try warm ethanol (I would have tried 70% ethanol at 50 degrees C). Remember to add ethanol to the control culture.
It is quite tedious to dissolve such fatty acid but by keeping FBS pre warm upto temperature about 50 degree C or a bit more under continuous stirring, we can dissolve palmitate in FBS.