Okay, so updates on those.
The "flying kick" was easy to figure out, if I'd ever stopped to read the actual in-game controls. Attack+Jump at the same time, and it could be useful if you're being surrounded, but has a long enemy recovery time like the jump kick.
For the bat, I'm thinking that it may not actually have been a bat stolen from an enemy, and that my memory isn't as good as it used to be. Tonight I did a little playing around in Beating Heart and found a couple drops where a bat could be picked up. This wasn't consistent though. Might be health-related? Or could just be buggy too, because in a couple instances I could see the bat for a frame and then it disappeared.
https://gfycat.com/recentgoodnaturedbelugawhale
I'm not sure how useful the bat would actually be during the run. It's a pretty slow attack that seems to effectively do the same as a jump kick with the immediate knockdown.
It's not looking like I have a recording unfortunately. I honestly hadn't thought about it again until submitting last night's run, which is when the question came to mind. I'll probably spend some time next session exploring combos to try to recreate it.
Separately, in last night's run I had a flying kick with a different animation than the standard one, again something I hadn't seen before. Same story though, not sure on inputs or if it's just a proc.
In one of my runs, I was able to steal a bat from one of the enemies in Beating Heart. I haven't been able to figure out the inputs to replicate this again. Anyone have any ideas on how this could be done?