Can I use household drain cleaner in my RV drain?

I wouldn’t. I’ve seen some argue that RV plumbing is the same as home plumbing, but if you have a clog, it’s easier, faster, and more effective to use a tank rinser, like this Camco Tank Rinser.

Also, preventative maintenance, like using LOTS of water when you use the toilet and leaving the black tank closed until you empty will help prevent clogs from happening.