Reflux in any non-polar aliphatic solvent is generally the best means. Hexane is the standard one, but I prefer heptane as it's safer to work with.

Par des solvants apolaire, comme Ether de pétrole, hexane, éther di ethylique . Bon courage 

Accurately weighted portion of each sample is homogenized in cold 154 mM NaCl. Total lipids, added internal standard (heptadecanoic acid or nonadecanoic acid) 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 methylated with 14% BF3 in methanol. The resulting FA methyl esters are extracted with hexane and analysed by capillary gas chromatography. 

Christie has some tips here in section F. 4 (link below), which is isopropanol first followed by chloroform/methanol.  Apparently straight chloroform/methanol will allow enzymes in plants to degrade lipids .  A straight nonpolar solvent (hexane) that some have suggested will do great job for triacylglycerols, but will leave some of the polar lipids.  Polar lipids may be minor in plants, but it depends on your research interest.  

http://lipidlibrary.aocs.org/topics/extract2/index.htm 

Fatty acids are mainly soluble in hexane, petroleum ether. Dichloromethane can be used but is a non-specific solvent. Whether in plants or stomach contents, the sample should be dry, otherwise the solvent does not "dip" the sample. Grind the sample increases the extraction yield. The separation and identification of the extracted aliphatic content can be effectively made by GC-MS after silylated sample. The alkaline hydrolise with KOH or is necessáry only if you intend to analyze the compounds that exist in the sample in free form and differentiates them from queexistem the sample in esterified form. You can see the references Food Chem 2014 165 330 and Nat Prod Res 2008 22 975.

Dear Teresa Valencak,

I had obtained faaty acids from plant, both in oily and solid form. the procedure i adopted for plant material was same as general extraction i.e, the dried plant material was extracted by methanol for thrre times without heating. the extract was fractionated by hexane and others. from hexane fraction, by column chromatogaraphy, using hexane: chloroform as solvents up to 20% chloroform and 80% hexane, i get oily fractions containing upto 40 fatty acids, after characterization by GCMS. from the same column, upto 40 % CHCl3:Hexane, i get six other fatty acids. i did not find these in any other fraction of my plant..

Dear Teresa Valencak,

You should try it by using Hexane, Petroleum ether and Chloroform solvent and than use column chromatography technique as mentioned by Hameed Shah.

just macerate the target by hexane for three days and you will get your fatty acids

simple and fast

As previous colleague said use hexane or petroleum ether, these solventes  

In most of cases they used non-polar solvent like petroleum ether, hexane.....

The most non-polar solvent is used for crude extraction of fatty acids

The solvent for greater yield is n-hexane

Pet-ether (not neuro-toxic)

We use this procedure from lyophilized samples to extract and quantify fatty acids of diets. I think this could be useful.

Article Rapid method for determination of total fatty acid compositi...

The most useful procedure will depend on what it intends to do with the extract obtained and the initial sample.You should also think about whether you want only fatty acids or also other types of lipids, such as triglycerides and phospholipids. From the dried or lyophilized plant, to obtain fatty acids, long chain alcohols, alkanes, sterols, etc. it is best to extraction with hexane or petroleum ether.

If is fresh plant, it is best to prepare a acetone extract and, after evaporation of the acetone, preparare a hexane fraction of the acetone extract.

If you want to analyze the hexane extract composition in fatty acids and other lipids is most effective using GC-MS after derivatization (for examplo sylilation) and use a cappylar column DB-1 type.

You can see how do that, and the results obtained in two diferente plants in the following publications.

Methods of Extraction of fatty acid or oil from plant seed or materials is similar or differ as every one explained use non polar solvents but i would like to know the extraction of fatty acid from extracted oil by heat/cold process from pant materials. kindly let me know in detail.