can I use 1/4" J Channel to mount 3/16" thick mirror?
A mirror that big will have some flexibility if there is some room behind it. Especially when you press on the mirror such as when cleaning it. 

I would recommend using a padding technique on the back of the mirror to give it a firm seating against the wall whilst at the same time causing it to flush out against the front inside edge of your J channels. 

The technique I would use would be to get some 1" wide foam type tape that has glue on just one side. Stick short strips of this to the back side of the mirror near the edges and at various points in the middle area. If one layer of the tape is not thick enough then simply place additional strips directly on top of the first set to increase thickness. 

The 1" wide foam tape should be available at most hardware and home supply outlets. Do select carefully as foam tape with glue on both sides is also common.