Do I need a Thunderbolt display adapter or should an older mini DisplayPort adapter work?
No, such an adapter does not exist and is unnecessary. Since Thunderbolt is backwards compatible with Mini Display port.   If you look at accessory options for the MacBook Pro, you will see only the following display output adapters available: 


  
  Apple Mini DisplayPort to DVI Adapter
  Apple Mini DisplayPort to Dual-Link DVI Adapter
  Apple Mini DisplayPort to VGA Adapter
  


So Mini DisplayPort is the correct adapter type. However, there are two DVI adapters to choose from. It depends on what display your are using and if it needs a single link or dual link DVI connection.

Generally speaking computer displays with a native resolution less than or equal to 1920 x 1200 are single link DVI, while displays larger than 1920 X 1200 are dual link DVI. Check your monitor's specification and requirements to be sure.

If you have the right resolution settings and adapter and the flicker persists I would trouble shoot and rule out each piece of hardware to figure out where the problem lies.


In the display
With the adapter / cabling
With the MacBook Pro