Can I use sunflower oil in oil paint?
Cooking oil certainly isn't a direct substitute for linseed oil. Oils used for paint and treating wood are so called 'drying oils' this means that they naturally polymerise when exposed to air, forming a dry flexible material. 

All vegetable oils will do this to some extent but for something like sunflower oil it will take a very long time and you will end up with a gummy sticky mess long before it actually dries. It is also likely that during this time it will end up being colonised by bacteria, turning it rancid. 

Also many drying oils are further treated by steaming (ie boiled linseed oil) and/or adding drying agents to speed up the drying process.