Okay, I'm guessing you don't usually do organic chemistry Daylan. Either way, it is clearly important that you get hold of a basic textbook on organic chemistry and look up chirality.
I must admit I don't work with biomolecules* but we can work a few things out just by looking at the molecules you're working with. First up, is dinitrophenyl isocyanate chiral? A simple rule of thumb in organic chemistry is to look for a carbon that is bonded to four different groups. This by itself might not be enough (the real rule is whether or not the molecule has a symmetry plane) but it's certainly good enough for 3,5-dinitrophenyl isocyanate. If you look up the structure on Google, you'll see that no atom is bound to more than three other atoms. That means that it cannot be chiral.
The next thing to consider is whether or not your derivative will be chiral. For this, you need to understand the reactants, the products and the mechanism of the reaction you're performing. Your reactant, a diglyceride, contains one chiral carbon 'in the middle'. It's chiral because it's bound to four different groups (the two different tails, one short alcohol and one hydrogen). But when you react with 3,5-dinitrophenyl isocyanate, you're modifying the oxygen of the OH group, not the chiral carbon. This means that you won't change the chirality of your reactants by making the derivative with an achiral molecule like 3,5-dinitrophenyl isocyanate. So if you start with enantiomerically pure DAG, you're going to finish with enantiomerically pure DAG.
You only need a chiral column if you're separating enantiomers. This means that if you're starting with a mixture of DAG enantiomers, you will need a chiral column but if you're starting with a pure enantiomer (and I guess you are) then you won't need a chiral column. If you want to use a chiral column on enantiomerically pure products, it should still work, it will at least separate your reactants from your product, but chiral packing is not necessary.
* i.e. I might have misread what you're trying to do.