With your symptoms it is definitely not the Hazard Flasher Unit or the Multifunction switch! both of these units direct power to right indicators and to left indicators with no respect to whether or not they are up front or at the rear. In other words the front indicator is in parallel with the rear indicator on each side.
The grounds though for front and back are different.
Are you saying that both bulbs on the RHS are flashing rapidly?
Is this a CRD or a Gasser? The 2006 CRD has a problem whereby the Fuel Filter Head Assembly Mounting Bracket can clamp down on the wiring harness causing wires to short to Chassis or to other random wires.
An indicator bulb flashing rapidly means that the Flasher Unit has sensed a reduction of current in that side regarding the connection of +12 volts between front and rear..in other words the front and rear bulb should have a common +12 volt connection between them as I stated ...in this case this common line is faulty or the ground is bad.
Use the Wiring Diagrams to trace this wire from front to back...could be a bad connector inline or the wire is open-circuit somewhere or a ground is missing...add your own temporary ground to the failing bulbs.
Download the 2006 Jeep KJ here...Section 8W has the Wiring Diagrams. The Index page has a Component Index where you can find the pages for Flasher Unit, Multifunction switch etc.
My Export 2002 CRD had a front end collision...I had to pull off about 15 wiring problems after that...wires were broken or shorting to ground/chassis or some other random wire.
I will look through the diagrams and direct you where to put your meter!
Page 8W-52-4 shows that a White/Orange Stripe wire goes from front to rear Right Turn Bulb....through several connectors. Ground is Black. You will see how the Flasher Unit supplies +12 volts to this common wire.
www.colorado4wheel.com/manuals/Jeep/KJ/