From someone who used them every day for the best part of a decade as part of a felling team about 20 years ago.
Yes, proper stuff is anti fling. Yes it's expensive.
As with many trades, the professionals are mixed in their approach to "the proper stuff". Many buy the proper stuff, and our ganger had a 45g drum of chainsaw oil - but many people used cheap engine oil, including one old chap that used to filter used engine oil through his wife's tights. Apart from a black chaincase, it didn't seem to cause any problems. Although the worm gear in the drive is often plastic so any metal scraps might cause wear, it wasn't noticable.
Would veggie oil work? Sure. Would it cause problems? Unlikely imo - maybe in heavy logging it wouldn't cool as much as a mineral or more viscous oil. The oil is used very briefly in most uses. In heavy use the pump output blocks and your chain goes dry quickly, but if you're familiar with your tool you'll notice the visual difference, the sound and the ability to cut all change very quickly as it dried out and heats up. For the occasional chainsawing I do now, I use engine oil - although it's obviously not as eco.