This is not my speciality but would still love to answer this question. I am from networks background and not fire fighting.
The edible oil fire comes under class F/ Class K depending on the region you stay.
The extinguishing methods are1. Dry CO2 for Small Fires2. If fire is large then methods like
A) Mechanical Smothering
B) Saponification.
For your case I would prefer Saponification if in household
in industry level dry CO2
Hope I answered your question
