I bought the SmartThings Button and am probably going to return it as it almost never works when you press it (usually have to multiple times), but can you not control a scene with it? If I use the built in Button SmartApp thing it only lets me turn lights on or off, not actually set the levels. I tried a 3rd party one I added through IDE but it was the same. I could use WebCore but never had much luck with that and just assumed something so basic as running a scene would be supported out of the box, but doesn’t appear to be?
It should work in the official smart lighting feature in the V2 classic app or as a custom automation in the new V3 app. No custom code or webcore required.
Which version of the app are you using?
FAQ: how to tell which version of the SmartThings mobile app that you have
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Also, “trigger a scene“ has a specific meaning in smartthings. A scene is a snapshot of a moment in time with multiple different devices. So you might have lamp A at 50%, lamp B off, and lamp C at 100%.
Say you call that scene “television time.“
You should then be able to create an automation so you will be able to press the button and activate that scene. But note that that does not mean real time dimming of any of the lamps. It just means re-creating that snapshot.
If instead you mean you want to hold down the button and have that change the dimming level, then no, the SmartThings button does not do that.
There are some other battery operated devices that can dim. See the Buttons FAQ:
Some of the devices are mains powered, some are battery powered, some are limited to specific regions, so read the descriptions carefully.
The buttons FAQ is just intended to have one or two posts per device. Each post should have a link to a conversation thread about the device. So please do not post any follow up on questions about devices in the FAQ – – either go to the conversation thread, or come back and post a question here and people will try to help. 
FAQ: Full list of buttons and remotes confirmed to work with SmartThings