Also, what operating system are you using?
At the very minimum you can increase the number of uploaded files by using the --transfers flag. For example, rclone copy remote1:\ remote2:\ --transfers 15 -P will allow you to transfer 15 files at once from one terminal window. The -P flag allows you to see progress in real time.
If you are new to rclone you should really familiarise yourself with rclone commands and rclone flags.
Another thing you might try is to increase the buffer size per file with --drive-chunk-size. For example, rclone copy remote1:\ remote2:\ --transfers 15 --drive-chunk-size 128M will increase the in memory buffer size per file from 16M to 128M.
Lastly, you should create your own Client ID, see the bottom of this document for explanation and instructions.
Apparently, according to the information that Harry referenced, uploading multiple chunks simultaneously to Google is currently not supported by Drive API.