Grounding my dishwasher
The printing on the wires indicates THHN style wire, and suggests pretty strongly that this is using the EMT conduit wiring method.  As such, the EMT is the ground, and we have several ways to tap it. 

First, if the geometry lines up, you can install a junction box at that point.  You use a standard EMT connector (e.g. this) to enter the junction box.  On the other side you enter with the standard "BX into junction box" connector.    For the ground wire, you land that on the ground screw on the junction box.  The box itself carries ground via the EMT connector to the EMT.  

Another way is to put a ground clamp around the EMT.  That will remove the necessity of a junction box.  I would run this ground wire outside the BX, because I don't see a way to exit the BX without a junction box.  

Now I agree with ThreePhaseEel that it's a mistake to go "straight-in" to the EMT. You should probably make a 90 degree turn into the BX.  A junction box can cover that, but another option is a 90 degree EMT elbow. They come either with side access or top-bevel access. Use ones with female threads on both sides, so you can screw in both of the above adapter types. 

I am not familiar enough with the question of whether you can use the BX flexible metal conduit as the grounding path, so I will leave that question to others.