Though you cannot view all available channels, you can anchorage the CSCC (Configuration System Chaincode) GetChannels API to get a list of those channels that clients are eligible to. All you need to do is invoke the chaincode that goes by the name CSCC.
Considering NodeJS the request will look as:
const request = {
chaincodeId : "cscc",
txId: 213213123123, // Some random transaction id
fcn: "GetChannels",
args: ['']
}
You also can also perform the same action with peer CLI:
peer channel list