I agree with everything Rod has said-free fatty acids by GC is not advised. However, if you do have to do it, I would say that the weakest point in your method is that you appear to be trying to do some sort of split or splitless injection into a packed liner. This procedure just adds another level of difficulty to your analysis, because these acids will stick to anything. You have an extra step in that you need to transfer your acids successfully from this liner to the column.
As Rod says, if your machine will take a packed column, you could put this in. Then you can inject directly onto the column with the needle inside the column, and if you are very careful, you may get this to work, especially with the columns Supelco make for this analysis. Alternatively, you could use on-column capillary injection-but this needs a different kind of injector to the one you are using. Here again the needle penetrates the column itself, and you have eliminated the problem of this intermediate step. I have got both of these methods to work (eventually). I prefer packed columns, because they are more resistant to the dirt that necessarily is introduced into the column along with your acids in both injection techniques. But the best suggestion is LC.