You should try running the debug version of flashplayer when testing, it makes sorting this kind of thing out much easier..

When I run your code it's as Wilbert suggest I get an error that outcheck1 is not definded

If you want to access variables outside of the function you just declare (create) them before the function

Code:
import km.core.*;
import km.components.*;

var outcheck1:String
var outcheck2:String
var outcheck3:String

checkbox1.setProperties({x:50, y:50, checked:false});
checkbox1.text = 'Checkbox 1';
checkbox1.onChange = function(){
outcheck1 = this.checked ? 'checkbox 1 checked' : 'checkbox 1 unchecked';
txt2.text = outcheck1;
}
addChild(checkbox1)


checkbox2.setProperties({x:50, y:70, checked:false});
checkbox2.text = 'Checkbox 2';
checkbox2.onChange = function(){
outcheck2 = this.checked ? 'checkbox 2 checked' : 'checkbox 2 unchecked';
txt2.text = outcheck2;
}
addChild(checkbox2)


checkbox3.setProperties({x:50, y:90, checked:false});
checkbox3.text = 'Checkbox 3';
checkbox3.onChange = function(){
outcheck3 = this.checked ? 'checkbox 3 checked' : 'checkbox 3 unchecked';
txt2.text = outcheck3;
}
addChild(checkbox3)

// output checkbox combinations

pushbutton1.addEventListener(MouseEvent.MOUSE_DOWN ,outputshow);

function outputshow(e:MouseEvent):void {
var result:String = outcheck1 + outcheck2 + outcheck3;
txt1.text = result;
}