The scenario you specify isn't very likely to happen. The food in an oven has a very low temperature. A casserole or loaf of bread might get some surface charring after staying for too long in the oven, but it'll need at least half an hour above the normal time for somebody in the next room to notice the smell. And there won't be much smoke and certainly no fire.
A common kitchen scenario is to forget something on stovetop. There you have several nice possibilities, depending on the amount of damage or chaos you want in the scene. A pot of something high in sugars, like jam left to cook down or caramel in the making (before adding milk) will result in charred residue which will smoke and stink a lot, ruin any coating on the pot (enamel, non stick) and annoy the cook to no end, but won't do any damage outside of the pot, so it can be hidden after five minutes of airing the kitchen. Or you can have milk boil over, it will happen in mere seconds, then it will then stick to the stove and the residue will be very hard to clean. Note that if you specified "baking" because your character is working in a bakery or as a patisserie chef, he will still be heating milk, jam and caramel frequently.
If you want actual flames, there's nothing better than oil. It will need longer time to get to auto-ignition temperature, but if you have somebody deep frying stuff on stovetop, and the person is not so great at managing temperature, it can happen right in front of the cook, without any need for forgetting. With a gas stove and a pan full of hot oil, you can also have a spark getting into the pan without the need for badly controled temperature. This kind of grease fire is quite dangerous, and shouldn't be extinguished with water.
If it absolutely has to be an oven, you'll have better luck if it is happening in a restaurant. There, you can find pizza ovens going up to 450 Celsius, or even wood fired ovens which are much hotter. A rotisserie with open heat elements is also a candidate, if you let hot fat drip on the lower elements. In a home oven, a broiler will have enough temperature to burn something to the point of lots of smoke and charring, but I doubt that you will get flames. I think that a forgotten creme brulee will be very good for this scenario - the burning sugar will give you lots of stink, and it's done on a broiler by default.
There are also self cleaning ovens, and if your character forgets food inside the oven before turning the cleaning cycle on, it can cause a fire, and a dangerous one at that, because you can't open the oven to extinguish it before the cycle is over. But you need a very scatterbrained character to pull it off.