Can the relative # of double bonds in fatty acids (in oils) be estimated by adding bromine to oil?

I would say so....bromine undergoes an addition reaction with a double bond. The reaction would be, for example:

C2H4 + Br2 -----> C2H4Br2

Therefore, every two equivalents of bromine used up means that 1 double bond has undergone an addition reaction.

There are a few things that you should do, first of all, to ensure that the reaction gives you accurate results. To make sure that there are no side reactions, I would carry out the reaction under anhydrous conditions (water-free), and I would also protect the acyl group on the carbonyl portion of the moleule (perhaps with a THP ether).

Now, when it comes to the actual procedure, I would add bromine to the acid in a titration. Basically when the brown bromine stops being used up, I would stop (i.e, that would be my endpoint). By doing this, and looking at the amount used up, you can take the ratio into account and figure out the number of double bonds. (Make sure that the bromine sln is of known molarity).