Question: I have a Metz AF 52 flash and a Nikon D5200 camera, which has no wireless commander.
Will a Yongnuo trigger work?

Answer: 
I'm using a Nikon 750 with a Yongnuo YN622n-TX transceiver attached to the hotshoe. I have a Metz 44 AF-1 attached to a YN622n II and set to TTL. 

When using Nikon cameras, the flash must be set to TTL! Everything works fine. I set the zoom on the TX to AU (automatic) and the zoom on the Metz matches the zoom on my lens. I can put the TX in manual mode and it also works, but the TX has more setting in manual mode than the Metz so there is a limitation there.

I have a Yongnuo YN568EX in another group and it functions perfectly.
I've seen posts that says you have to turn everything on in a specific order or the radio transmission fails. I can turn everything on in any order I like. 

After everything is on I half-press the shutter button on my camera a couple of times and everything is good.

I have the version II of the trigger so that may be the difference. If you have version one of the trigger then you might want to upgrade to version 2. I have also updated the firmware.
Please note that the Metz Mecablitz 64 AF-1 flash has a radio receiver, but it does NOT work with the YN transmitter.  

According to the flash manual (page 191, "Remote Slave Flash Mode"), it's compatible with the Nikon "Advanced Wireless Lighting" system, which apparently is different than the YN's system.   
BTW, the Nikon SU-800 is $337 in the U.S., while the YN-622N-TX is about $44...