add this to your uses
{$IFDEF DARWIN}MacOSAll, appkit,{$ENDIF}
on form creation put this:
{$IFDEF LCLCarbon}
NsApp := NSApplication.sharedApplication;
{$ENDIF}
when you need to make the icon bounce use this for bounce the icon once
{$IFDEF LCLCarbon}
FRequestUserAttentionID := NSApp.requestUserAttention(NSInformationalRequest);
{$ENDIF}
or this to bounce icon untill application is activated
{$IFDEF LCLCarbon}
FRequestUserAttentionID := NSApp.requestUserAttention(NSCriticalRequest);
{$ENDIF}
if you need you can use the FRequestUserAttentionID identifier (it's an integer) to deactivate the bouncing
{$IFDEF LCLCarbon}
NSApp.cancelUserAttentionRequest(FRequestUserAttentionID);
{$ENDIF}
p.s you can't bounce icon if your application is active (it has 'focus')
p.p.s. i'm using $IFDEF to be prepared to compile this code also on other platforms.