Millennials aren't really more cocky or disrespectful than other generations. Remember the Boomers saying, "You can't trust anyone over 30"? The generation gap has never really left us. I'm part of Gen X. I came out of school thinking I knew better than some of the people who were my managers.
You know what? In some ways I was right. I remember speaking to one of the VP of Sales at the first company I worked for. I told him I wanted to learn Mandarin because China would become an economic superpower and I said that India represented a massive opportunity for economic development. He vehemently disagreed, saying that the then formed EU was the true economic opportunity that industry should focus on. I wish that discussion was an actual monetary wager because I would now be retired and relaxing on a beach.
My point is this, those youngsters may have very valid ideas and might have better ideas than their older teammates. If you treat them as a source of innovation and approach them as a servant-leader/mentor you will gain their respect. Press home the idea that you want them to be contributors to the success and future leaders of the organization. These "kids" have a huge amount of energy and desire for recognition. Harness that.
Here are some steps that can help you foster a dialogue and shape some behaviors:
1. Make sure that your culture actively rewards and recognizes respect for coworkers, humility and collaboration.
2. Identify an issue within the company that could use some fresh perspective. Form a task force around it comprised of those millennials and an older leader who can help them get their solution to the issue reviewed and implemented. This will give them a sense of ownership in the organization and help satisfy some of that millennial desire to be recognized.
3. Immediately address negative behavior in private. Praise positive behavior publicly.
4. Provide a forum where young teammates can voice opinions and talk to the organization’s leaders.