The amount of I and Cl can be determined by argentometric titration. The AgI precipitates first, followed by the AgCl. A silver wire electrode is used to follow the titration, using a pH meter and standard reference electrode to make the actual measurement.
The example is a hoary old classic found in many analytical chemistry textbooks. You should find it there.
Here's another one. Get a table of solubility products, and find the Ksp's for the chloride and iodide of the same metal.
If the Ksp's are separated by three or more orders of magnitude, it will be easy to separate by fractional precipitation.
Finally, you can convert the iodide to iodine with a weak oxidizing agent, extract into an organic solvent, and reconvert to the iodide again.
Dangerous Bill