Why do you think he is current CiC. If we are under COG right now ( I think likely ) Northcomm assumes the role and designates someone.
The fencing around WH but not SCOTUS or the Capitol adds confidence we are under COG. Now they are boarding up buildings near WH. Any street that leads to the WH is under federal jurisdiction not the mayors. Park services is leading the fencing and boarding. They normally wouldn't have jurisdiction for these areas but they are part of a Joint task force capitol region. That is under the command of northcomm. Nancy passed a bill for a limitless slush fund to protect the capitol region before she lost the speakership.
I don't think any Joint Chief can be appointed CiC in a COG situation. They leave service by retirement after this position.