The same as in JavaScript, using Array.prototype.indexOf():
console.log(channelArray.indexOf('three') > -1);
Or using ECMAScript 2016 Array.prototype.includes():
console.log(channelArray.includes('three'));
Note that you could also use methods like showed by @Nitzan to find a string. However you wouldn't usually do that for a string array, but rather for an array of objects. There those methods were more sensible. For example
const arr = [{foo: 'bar'}, {foo: 'bar'}, {foo: 'baz'}];
console.log(arr.find(e => e.foo === 'bar')); // {foo: 'bar'} (first match)
console.log(arr.some(e => e.foo === 'bar')); // true
console.log(arr.filter(e => e.foo === 'bar')); // [{foo: 'bar'}, {foo: 'bar'}]
Reference
Array.find()
Array.some()
Array.filter()
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