Starch gives a positive reaction with iodide, when the later is entrapped in the helical 3D conformation of starch (See attached picture). so you have three possibilities:
1. Iodide does reach starch molecules to reach with
2. Starch does not keep it's helical structure, it can't entrap iodine molecules
3. More obvious, if you have unsaturated fatty acids in the emulsion, they have more affinity (double bonds) to react with iodine.
The starch helices can not only entrap iodine, but also fatty acids and other hydrophobic molecules. It is quite likely that the large amount of lipids outcompete the iodine for complexation with the starch.
Iodine forms inclusion complexation with amylose which results in the blue color. Moreover, fatty acids also form the same type of complexation with amylose; however the rate of the complexation depends on the length of the carbon chain of the fatty acid and DP of amylose, and if the fatty acid is saturated or not. Based on this, there is a competition in the formation of inclusion complexation with amylose in the presence of different guest molecules, in this case: iodine and fatty acids.
The above answers are spot on. Two additional points.
1. It depends on what your "starch" is. To get a good blue color, you need amylose chains of 10 to 20 glucose units. Waxy starches and soluble starch hydrolysis products often contain only short chain or branched materials that cannot bind iodine. Check your starch before adding the oil. If it is negative for iodine, this is the problem. If the starch is positive, the problem is most likely the following.
2. The iodine color is due to the partitioning of the iodine from the aqueous layer to the hydrophobic inner region of amylose coils. Fatty acids will form complexes with amylose chains, but not triglycerides. The oil phase, being hydrophobic, will take up the iodine preferentially, preventing complex formation.
To develope amylose inclusion complexation, an amylose chain with DP of at least 18 is essential which results in 3 turns. If inclusion complexation with a carbon chain, like fatty acids, most of the researches show at least 10 carbons; however few reveal that this complexation with butyric acid (4 carbons) are also possible (see the research and review papers of Joke A. Putseys).
In case of starch hydrolysis and its association with the presence of amylose inclusion complexes, I address you to my papers. There you will find detailed researches on the formation of amylose inclusion complexes in order to develop slow and resistant starches.