RPM dropping and going back up and down with light acceleration?

Thanks for the video, yep that is not normal and the slight noise it is making is not good either, also I noticed the check engine light on so we should run the codes to see if any are for the transmission which can further the diagnosis. Here is what I would do first:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

They will read the codes for you at AutoZone, then get back to me so we can figure out what to do. To me it sounds like the transmission is defective but let's get the codes first.