I would like have a Krink in 5.56 from my own gun. Really fond of the wood stocks I just want the short barrel. I think it would look pretty cool. Is this possible?

It's possible, but requires a ton of different parts than what you have on your gun. You might want to consider an AK102 which is shorter than the standard AK and would use more of the parts you already have, or the Romanian AIMR which is a carbine similar to the Krinkov. Kvar has the necessary gasblocks for both right now.

You should build it out of a 5.45.

Even if the side of my gun says 5.56.

I used a Norinco 84S (,223) for my Krink build...

Purists prefer the 5.45 round since that's what it was made in originally. I prefer 5.56/.223 for logistics reasons (These points have been covered in numerous threads by others already.) so I can understand you wanting to use the SAR3 you have. The SAR 3 has some differences, in that it uses a 7.62 carrier and 5.45 bolt. I don't know if the ejector rails are 7.62, and if so I don't think your SAR3 receiver would work for that. The 5.56 models are kinda bastard children of the AK world, using different parts to get the job done. The SAR3 isn't as interchangable as a Bulgarian 5.56, which also makes the appeal of the 5.45 to people as it's all AK74 parts then. You still planning on going the short Krinkov route, or you considering the AK102 type series? You'll get better ballistics in a package only slightly longer....