How to format the output of kubectl describe to JSON

kubectl describe doesn't support -o or equivalent. It's meant to be human-readable rather than script-friendly. You can achieve what you described with kubectl get pods -l <selector_of_your_rc> -o <output_format>, for example:

$ kubectl get pods -l app=guestbook,tier=frontend -o name
pod/frontend-a4kjz
pod/frontend-am1ua
pod/frontend-yz2dq

Based on the output of kubectl help describe, it looks like it does not support structured output:

$ kubectl help describe
Show details of a specific resource or group of resources.

This command joins many API calls together to form a detailed description of a
given resource or group of resources.

$ kubectl describe TYPE NAME_PREFIX

will first check for an exact match on TYPE and NAME_PREFIX. If no such resource
exists, it will output details for every resource that has a name prefixed with NAME_PREFIX

Possible resource types include (case insensitive): pods (po), services (svc), deployments,
replicasets (rs), replicationcontrollers (rc), nodes (no), events (ev), limitranges (limits),
persistentvolumes (pv), persistentvolumeclaims (pvc), resourcequotas (quota), namespaces (ns),
serviceaccounts, ingresses (ing), horizontalpodautoscalers (hpa), daemonsets (ds), configmaps,
componentstatuses (cs), endpoints (ep), and secrets.

Usage:
  kubectl describe (-f FILENAME | TYPE [NAME_PREFIX | -l label] | TYPE/NAME) [flags]

Examples:
# Describe a node
kubectl describe nodes kubernetes-minion-emt8.c.myproject.internal

# Describe a pod
kubectl describe pods/nginx

# Describe a pod identified by type and name in "pod.json"
kubectl describe -f pod.json

# Describe all pods
kubectl describe pods

# Describe pods by label name=myLabel
kubectl describe po -l name=myLabel

# Describe all pods managed by the 'frontend' replication controller (rc-created pods
# get the name of the rc as a prefix in the pod the name).
kubectl describe pods frontend

Flags:
  -f, --filename=[]: Filename, directory, or URL to a file containing the resource to describe
  -l, --selector="": Selector (label query) to filter on

Global Flags:
      --alsologtostderr[=false]: log to standard error as well as files
      --certificate-authority="": Path to a cert. file for the certificate authority.
      --client-certificate="": Path to a client certificate file for TLS.
      --client-key="": Path to a client key file for TLS.
      --cluster="": The name of the kubeconfig cluster to use
      --context="": The name of the kubeconfig context to use
      --insecure-skip-tls-verify[=false]: If true, the server's certificate will not be checked for validity. This will make your HTTPS connections insecure.
      --kubeconfig="": Path to the kubeconfig file to use for CLI requests.
      --log-backtrace-at=:0: when logging hits line file:N, emit a stack trace
      --log-dir="": If non-empty, write log files in this directory
      --log-flush-frequency=5s: Maximum number of seconds between log flushes
      --logtostderr[=true]: log to standard error instead of files
      --match-server-version[=false]: Require server version to match client version
      --namespace="": If present, the namespace scope for this CLI request.
      --password="": Password for basic authentication to the API server.
  -s, --server="": The address and port of the Kubernetes API server
      --stderrthreshold=2: logs at or above this threshold go to stderr
      --token="": Bearer token for authentication to the API server.
      --user="": The name of the kubeconfig user to use
      --username="": Username for basic authentication to the API server.
      --v=0: log level for V logs
      --vmodule=: comma-separated list of pattern=N settings for file-filtered logging

In my case, I needed to get the load balancer address from the service. I did it using kubectl get service:

$ kubectl -n <namespace> -ojson get service <service>

{
    "apiVersion": "v1",
    "kind": "Service",
    [...]
    "status": {
        "loadBalancer": {
            "ingress": [
                {
                    "hostname": "internal-xxxxxxxxxxxxxxxxxxxxxxxxxxx-yyyyyyyyyy.us-east-1.elb.amazonaws.com"
                }
     [...]
}