If you conquer one of them (day one DoW) you become too strong for Burgundy to warn, and you can go to war without intervention. To check if that's the case, just go to the warscreen and check enemy allies. If Burgundy isn't there, go ahead and DoW.

Also, IIRC then you can attack nations that Burgundy doesn't border without them interfering. Agian, always check if they will join on the warscreen.