I do not recommend any drain cleaner as they can be iffy at times and there are some pretty easy things that don't need much more than a strong hand or possibly a cresent wrench or large pliers.
One of the problems with the chemical cleaners is that it can quiet easily kill the sepic system in campgrounds and that is NOT GOOD!
I did this snip from the parts catalog to show what I think has happened!
https://catalog.winnebagoind.com/menu/Parts.htm
Click this snip to get better view!
If the vanity sink runs but not the kitchen sink it tells us a lot. They both use the same main run, with the kitchen running along to under the vanity where they are joined with a tee.
So if the vanity drains okay that pipe to the holding tank is okay. But the long pipe from the sink is not very prone to clogs. Under the sink there is a drain trap which holds water full time and those are famous for stoppage/clogs!
Two ways to clear this common problem. One is a plunger like used to clear stool clogs or also any type drain. The rubber cup gizmo on a stick?
Set it over the drain so air is trapped and pump it up and down a few times to force water down and then as you let it up, there is a vacuum that tends to suck any clog upward. Most of the time it is easy to get it going!
But you might review what and why it is stopped up! Any chance there was something like hot grease, a tub full of crawdad tails, etc. put down the drain to clog it? Hot grease is one certain way to stop a drain as it hits the water in the trap!
I found college students just moving out on their own have missed that training!
But if it is a grease clog, those are not easy to clear as it has to have the trap pulled and then you find what looks like somebody fillled it with mashed potatoes! And you have to scrape it out!
That's where the wrench or pliers comes in!