Social media is about the best option for promoting your channel(s) to other people. Not only is it the best option, but its free!
Of course you could probably pay some professionals to help you get a game plan together and work on a campaign to grow your channel if you're a millionaire. I don't know where to start there though so I couldn't help. (lol)
Sites like this, Damnlag, that offer places where you can advertise your channel for free can help. However, you're not going to get huge results. Just being honest here. This site and other sites like it are more for sharing and discussing strategies like the one we're talking about now.
If you haven't already, create a Twitter and Facebook account and use those to promote your channel(s) and content. Follow other creators and channels that have similar interests of course. Reach out to your followers on Twitch, Mixer or YouTube now and get them to follow you on the social media platforms. Their support on those platforms will help you as well.
Use keywords, and hashtags on the social media sites to attract people searching for content such as that. When you go live on a game, for example Call of Duty. Use #CallofDuty #ModernWarfare #VideoGames or other similar topics related to the game.
Discord servers like ours can help you as well. You'll find some people willing to check out others channels and show their support within the community. Creating a discord server of your own for your own community to interact and game with you might even help your channel.