Dibond is an aluminium sandwich with a Polyethylene core. The burrs you are looking to avoid are therefore aluminium - I bet it isn't a nice free machining variety either. The left spiral will push the burr from the upper surface downwards. I'm not sure how the reverse will work on the lower edge unless you can machine an offset to the profile - 0.1mm might do for example - to stop the second tool from rubbing the first, finished cut. It's CNC after all, and a CNC control should manage a profile offset.

Do you have the opportunity to have a rigid sacrificial surface beneath the work piece? Are the edges supported well enough to be stiff and not flex in machining? Reply #6 points out the pitfalls accurately. Are your profiles much smaller than the raw material? Can you use tabs to stabilise the profile whilst clamping on the waste?

One strategy that may help is to use fewer flutes - single flute cutters are good for plastic, I'm not sure about sticky aluminium. Also to avoid excessive spiral angles - the longer the tool edge in contact with the work piece, the more friction raises the temperature and melts the local area, pushing a bigger burr as a result. Straight flutes have the lowest contact friction. High spirals tend to pump swarf along the tool - the burr tends to follow.

Can you get a good air blow onto the tool? Keeping things cool won't stop burrs but may reduce them, and it will reduce the chance for chips to link up and rejoin the cut.

Good luck.
D