Where do I connect the green wire on my dishwasher?
The flex is your grounding path, so cap off the green wire

In your situation, the metal conduit (flex, then rigid/EMT) is serving as the equipment grounding path, via the conduit fitting going into a 1/2" knockout (KO) on the dishwasher junction box, so you don't have a ground wire coming in.  This means you can simply cap the green ground wire off; if that's not satisfactory for some reason, you can use a grounding locknut instead of the existing locknut on the fitting, then attach the green wire to the screw on the grounding locknut.