How long can you store hot pepper oil? I made a small batch by heating extra virgin olive oil and then adding red pepper flakes.

Understand rancidity is a process, not a state. Being highly unsaturated, olive oil oxidizes relatively quickly releasing carcinogenic free radicals as it does so. The "extra virgin" variety is the most fragile due to its delicate nutritive components. Heating is not a good thing; it is even more unstable at high temperatures (acrylamide formation can occur around 300F). Refrigeration = good, high-temp frying = bad.

I like to use my olive oil within 6 months, a year from harvest tops.

My chili oil lasts almost indefinitely in the fridge. I make it the same way you do, except with cheaper olive oil. To be on the safe side, I would give it 6-9 months in the fridge.