I recently learned about oatmeal (quick oats) for WAMming. The thing I love about it is that it's so... thick! Is there going to be any issues with disposal if I just dump it in the bath tub. Any chance of the tub choking up?

Yes, if you try and flow that down the bath drain it will clog it instantly.

I'd suggest when finished, first dilute it by filling the bath to near the brim with water, mix it, then use buckets to scoop it into the toilet, and while you can just keep pouring the buckets in, flush it as often as the cistern re-fills too, you want as much water as possible in with it.

Or, if you're concerned the loo drain might clog, don't dilute it, instead line a large bin with several layers of heavy duty trash bags, scoop it all into that, carry the entire bin outside (don't try and liff the bags out in the house) and then lift them out and into a dumpster.

I saw Choke the Tub at Glastonbury in 1947...

Half fill a bucket with the mess, then top it up with water.
Swish your hand through it to break the mess down into free-flowing suspended lumps.
Pour down the toilet.

This is my go-to method, never blocked the loo- used crazy thick gunge, oatmeal, cakes/pies, clay etc.
Washing myself off can be enough to jam up the bath, so you really don't want it going down the plug hole if you can help it.

Sometimes it can work out ok if you thin it down enough and supervise it but to be safe, for oatmeal I hand scoop it back into the bucket, add more water and mix to thin it down, then flush down the loo

Which is what you will tell the plumber if the drain does block

"Why the hell did you put so much oatmeal in the toilet?"

*lie detector goes off*

*Plumber starts to snake the toilet and finds out what really clogged the toilet*

"What a liar, Im gonna charge him extra."

*knocks on wood*

I've had no problems sending oatmeal and pie crust down the shower drain. I usually take a long shower to clean off since that's where my sessions are anyway. The water thins out the oatmeal and I can break up the pie crust more if I need to. Afterwards I like to use a healthy dose of drain cleaner just in case!

Yes, ruined plumbing in three apartments by this point...

Quick-cook oats are thin enough that they eventually dilute in water. I usually use a combo of cake batter & quick-cook oats (plus water) for slime. When I'm done it usually all goes down the drain when I turn on the faucet. The only time there was a problem was when I used more than 2 buckets. (Two is usually my norm.) But even then I just gave it a little plunge & it all eventually went down.

Old-fashioned oats, on the other hand, WILL clog your drain! Don't use those (or steel cut).