Total lipids are extracted with chloroform/methanol (2:1). The chloroform phase is removed and evaporated to dryness under a stream of nitrogen. Total lipids are saponified with 2% KOH in methanol and the FAs are methylated with 14% BF3 in methanol. The resulting FA methyl esters (FAMEs) are extracted with hexane before injection to GC
Mhm. Is there a specific reason why you hydrolyze total lipids with KOH prior to BF3. Usually there is no need for KOH hydrolysis except your samples contain a high amount of lipids with N-bound FAs e.g. sphingolipids. Usually all glycerol and glycerophospholipids are hydrolyzed by BF3.
Am I right that you want to get rid of all free FAs and analyze all bound FAs?
Ok! The complete and quantitative removal of free FAs is tricky. I am not sure which analytical methods you can use but u can try different approaches.
1.) You can try an alkaline extraction (0.1-0.5% NH4OH) to shift the extraction coefficient of FAs to the aqueous phase. Vice versa you can force the FAs into the organic phase by protonating the FAs using 1% acetic acid. However alkaline solutions can easily drive hydrolysis of lipids, so you have to test for optimal conditions. Furthermore you have to check if all free FAs are removed, which can be done by silylation of free FAs. (therefore you have to check if your GC column can handle the silylation reagents)
2.) You can try solid phase extraction on silica or aminopropyl columns. There it is pretty simple to get rid of FAs but you will need some time to establish a proper protocol to be sure that all residual lipid species are quantitatively retrieved.
3.) You can split your sample in aliquots and isolate the free FAs using thin layer chromatography. Afterwards you can measure the isolated "free FAs" (from aliquot 1 as FAMEs) and total FAs (from aliquot 2 as FAMEs) and make a background correction. This method should give you reliable data if you do a proper number of biological and technical replicates.
Since I do not know your equipment I would try the third approach since the material you need for TLC is usually not really expensive and TLC method developement can be done pretty quick.