Doesn't that have to be mashed?
Yes. Rice needs to be gelatinised, which happens when you cook it. Then it needs to be mashed to convert the starch to sugars. Flaked rice is gelatinised during it's production, so it just needs to be mashed.
So if you are looking for something that you can just add to the fermenter, then the brown rice syrup will work, I don't know how much flavour will carry over into the beer, probably not a lot but you might get some of it. Googling, I did find something that looks more neutral - Melrose Organic Rice Syrup.
But let's just step back for a second.
You are using sugar syrup that just happens to be made from rice. It is neutral in flavour. The reason why rice is used in Asian and some American breweries is because that is their cheapest/easiest form of carbohydrate to get to make the sugar syrup. In Australia, the cheapest source is sugarcane, which is why Australian breweries use that neutral sugar syrup in their beers.
So if you are just wanting to use a neutral adjunct, it makes far more sense to use dextrose as it is far cheaper than buying jars of clear rice syrup and you won't taste the difference.
If you wanting to use rice because it is fun and a talking point then go for it. I've made a few rice beers but I am an all-grainer and I use boiled home brand rice in my mash tun. Great beers but the rice contributes no flavour and I might as well just add table sugar or dextrose to the boil.