You probably don't have a "debug" Flash Player associated with SWF files on your system. That's needed for OpenFL projects (by opposition with regular Flash projects managed by flashDevelop).
First make sure you have one installed: 
- in FlashDevelop select 
Tools > Install Software... 
- choose 
Flash Player SA (stand alone debug Flash player) 
- restart FlashDevelop.
 
Sadly for some complicated reason it isn't possible yet for FlashDevelop to tell OpenFL what Flash player to use even if you have it installed that way, so the next step is needed:
Associate the Flash player:
- in FlashDevelop select 
Tools > Program Settings... 
- look up the path in 
FlashViewer plugin > External Player path 
- now in a Window Explorer, locate some SWF file and associate this player executable with SWF files,
 
- when you double-click a SWF in Window Explorer it should open this program,
 
- verify when you right-click on the player that it has a "Debugger" item in the context menu.
 
Retry launching your OpenFL project in FlashDevelop, you should see the traces in the Output.
PS: to completely disable traces for release, edit your project.xml and add: 
<haxeflag name="--no-traces" />