Something is off. Thiosulfate and starch are used to titrate iodine, not dichromate. Straw yellow color is diluted iodine in water (and yes, that's the moment to add starch in iodometry), but there is no way to see it in the presence of Cr compounds, be it chromate, dichromate or just Cr3+, their colors are way too strong.
Original solution doesn't contain iodine. Apparently from your description there is a step before titration that is intended to produce iodine - but I have no idea, if oxidation of iodine to iodide with dichromate (especially in the presence of nitric acid, another oxidizing agent) is stoichiometric (and fast enough). Could be, I just don't remember such a procedure being discussed/mentioned.
Does the color of the solution change after adding iodide and HCl? If so, you can try to titrate this solution with thiosulfate till it gets close to the original color (before adding iodide), and try to add starch then.
You can even add starch much earlier, just to see if it changes the solution color. Normally you would want to add it as late as possible as the reaction between starch and concentrated iodine is a bit too strong and can make detection of the end point difficult, but if you add it earlier you will at least know if everything works correctly (just don't treat result of this titration too seriously, more as an indication when you are getting close to the endpoint and it is time to add starch in a "real" titration).