Iterating through nested array of objects
Your method already looks good! I would only make a couple small changes to the logic as follows: 


The if (this._children.length &gt; 0) isn't necessary as the for loop
will make the check for you
Instead of using a standard for loop, I would prefer a for..of
loop. Typescript will transpile this so it will work in any
environment
I prefer early returns to nested statements. Because of this, I
would recommend storing the result variable in as small a block as
possible


With these changes:

public findNode = (id: any): TreeNode =&gt; {
  if (this._id === id) {
    return this;
  }

  for (const child of this._children) {
    const result = child.findNode(id);
    if (result) {
      return result;
    }
  }

  return null;
}


Also, here's a couple Typescript specific notes:


Avoid any like the plague. When you use any you are telling
typescript to effectively ignore any mistakes in your code. Given
your data structure, it looks like id should be of type string
I highly recommend turning on
strictNullChecks.
This will help prevent a large class of errors
Methods are public by default in Typescript, with this in mind I
recommend dropping the public modifier in most cases as it is redundant. However, this does not apply if you are working on a team with developers who generally work with other languages as it could lead to confusion in the team. For example, in C# the default is
that all methods are private


With these changes:

findNode = (id: string): TreeNode | null =&gt; {
  if (this._id === id) {
    return this;
  }

  for (const child of this._children) {
    const result = child.findNode(id);
    if (result) {
      return result;
    }
  }

  return null;
}