Kubernetes - How to define ConfigMap built using a file in a yaml?

Your config.json file should be inside your mychart/ directory, not inside mychart/templates

Chart Template Guide

configmap.yaml

apiVersion: v1
kind: ConfigMap
metadata:
  name: {{ .Release.Name }}-configmap
data:
  config.json: |-
{{ .Files.Get "config.json" | indent 4}}

config.json

{
    "val": "key"
}

helm install --dry-run --debug mychart

[debug] Created tunnel using local port: '52091'     
                                                     
[debug] SERVER: "127.0.0.1:52091"                    
                                                     
...           
                                                     
NAME:   dining-saola                                 
REVISION: 1                                          
RELEASED: Fri Nov 23 15:06:17 2018                   
CHART: mychart-0.1.0                                 
USER-SUPPLIED VALUES:                                
{}                                                   
                                                     
...
                                                     
---                                                  
# Source: mychart/templates/configmap.yaml           
apiVersion: v1                                       
kind: ConfigMap                                      
metadata:                                            
  name: dining-saola-configmap                       
data:                                                
  config.json: |-                                    
    {                                                
        "val": "key"                                 
    }     

EDIT:

But I want it the values in the config.json file to be taken from values.yaml. Is that possible?

configmap.yaml

apiVersion: v1
kind: ConfigMap
metadata:
  name: {{ .Release.Name }}-configmap
data:
  config.json: |-
    {
{{- range $key, $val := .Values.json }}
{{ $key | quote | indent 6}}: {{ $val | quote }}
{{- end}}
    }

values.yaml

json:
  key1: val1
  key2: val2
  key3: val3

helm install --dry-run --debug mychart

# Source: mychart/templates/configmap.yaml
apiVersion: v1
kind: ConfigMap
metadata:
  name: mangy-hare-configmap
data:
  config.json: |-
    {
      "key1": "val1"
      "key2": "val2"
      "key3": "val3"
    }

Here is an example of a ConfigMap that is attached to a Deployment:

ConfigMap:

---
apiVersion: v1
kind: ConfigMap
metadata:
  name: jksconfig
data:
  config.json: |-
{{ .Files.Get "config.json" | indent 4 }}

Deployment:

---
apiVersion: apps/v1beta2
kind: Deployment
metadata:
  name: jksapp
  labels:
    app: jksapp
spec:
  selector:
    matchLabels:
      app: jksapp
  template:
    metadata:
      labels:
        app: jksapp
      containers:
        - name: jksapp
          image: jksapp:1.0.0
          ports:
            - containerPort: 8080
          volumeMounts:
            - name: config #The name(key) value must match pod volumes name(key) value 
              mountPath: /path/to/config.json
      volumes:
        - name: config
          configMap:
            name: jksconfig