Is there away to install a flip out radio and still keep my factor navigation 2004 G35 COUPE

 

First:
Flip-out will get in the way of the a/c controls if in the top of a single din conversion, or hit the shifter in the bottom of of a conversion. Moving parts are a point of failure I'd rather not have - Plus, single-din dash conversion kits are harder to come by than double din.
So flip-out single-din is a bad choice in the first place.

Second:
There's so many good double-din nav units out there that are exponentially better than the factory unit. In just about any price range.

Third:
You can't even get updated maps for the factory nav system anymore. Those maps are already 6+ years out of date now.

Fourth:
Most nav systems can display to a second screen to make use of the pop-up screen via the VCI-NIS1 (~$450) (cheaper elsewhere) to put the directions in a better view position, if that's one of your reasons to keep factory nav.

Fifth:
You'll lose audio from the factory nav system, unless you go through a complicated custom setup.

Sixth:
Between the double/single DIN dash kit, steering wheel control adapter, antenna adapter and wiring harness, you're out $300-500 (metra dash kit on the cheap end, JDM on the expensive end), not including labor. This is not a cheap conversion even if the head unit is free. Do it right with a quality unit, not the one that you have from your last car, or got handed down, or "found".

So, now that you've got the long answer, the short answer:
Yes, you can, but don't.