Can a VPN increase your internet speed? The answer is No.
Why not? VPNs are only a part of the medium through which you connect to the internet. But VPNs can and may improve your streams performance. They do so when the connection is channels to a more powerful and less congest server.
If the VPN server is located close to the country where the content you want to watch is and the server is not crowded, your streaming can be much smoother than streaming without a VPN connection.
Also, since VPNs help you overcome throttling issues by rerouting traffic through their servers, this may increase streaming performance slightly.