If your button is not a direct successor of the view controller's view (aka, the hierarchy is something like ViewController's View -> SomeOtherView->Button), you won't get the right math by simply using frames. You will have to translate the button's Y-position to the coordinate space of the window object or your view controller's main view.
Take a look at this question: Convert a UIView origin point to its Window coordinate system
let realOrigin = someView.convert(button.frame.origin, to: self.view)
Then apply the math suggested by Lucas Palaian.
let bottomSpace = view.frame.maxY - (button.frame.height + realOrigin.y)
Another work around, in case something really wild and wierd is going on there, is to drag and drop an outlet of the button's bottom constraint. (Select the constraint from the view hierarchy in Interface Builder, hold the control key and drag the constraint to your view controller.) Then in your code you can access the constant.
let bottomSpace = myButtonBottomConstraint.constant