How do I create a rotating zooming animation in premiere that I can loop seamlessly upon exporting?
I'll answer the question for After Effects, because to do it in Premiere would be a nightmare. Probably possible, but the survivors would envy the dead.

The tool you need is parenting. Parenting enables you to group layers together, so that what you do to a parent layer you also do to its children. It only works one way though, so the children can have their own lives, moving them wont affect the parent.

Ok so you'll need to put the two layers in a composition. The easiest way to do that is to stack them above each other in a timeline in Premiere, right-click and choose replace with After Effects composition. This will open up AE with a new comp (AE version of sequence) with your layers in it. Layers in AE work the same as in PP and Potatoshop, you view them from the top down. Put the inner layer (the one you want to see at the end) on top. Go to the end of the composition (hit end) and adjust it so that it fills the screen how you want it. You can just click on it in the comp window to manipulate it, but if you want to access the numbers, hit p (no command or control key, just the letter — that's how AE rolls) for position, s for scale, r for rotation or t for opacity. Shift will show multiple properties at once, or if you want to be a noob for your whole life you can just twirl down the arrows until you find the property you want. But you don't want to be a noob for the rest of your life, do you? I can't hear you. DO YOU?

 Don't you dare.

Ok so for your purposes you'll need all of the properties above. Hold Shiftand press prst as needed. Adjust them until your layer is in its final possie.

If you want to manipulate a layer in the comp window use v for the general select / move / drag-corners-to-scale tool, or to rotate it mash w, which will select the wotate tool. Or you could click on the tool panel and choose your tool, but you're not going to do that are you? ARE YOU? I'M WATCHING YOU. You can also scrub the numbers in the properties panel by click-and-dragging, or click and type if you know what you want. This works for any blue numbers in AE.



Now we need to make these puppies move, that's what animation is all about. To do that we need keyframes. Like PP AE uses keyframes to allow properties to be changed over time. To create a keyframe, if you're a noob, you click on the little stopwatch next to the property name. 



When the stopwatch is active it means that any changes you make to that property will create a new keyframe. There's a standard noob mistake which is to think that the next time you want to set a keyframe you have to click the stopwatch again. Don't do that, it will turn OFF animation for that property. Also, don't be clicking. [Smacks mouse hand] Stop crying and start learning the keyboard shortcuts like a pro. Seriously, your carpal tunnel will thank me in a few years, and you'll be waaay faster.

To set a keyframe on a property you press its keyboard shortcut but with shiftalt, or for those still using macs shift⌥/opt held down. You'll want to set a keyframe for all your properties, so don't just stand there, get keystrokin': shiftalt / ⌥p then  shiftalt / ⌥r, shiftalt / ⌥s, and  shiftalt / ⌥t. Practice it now and it will go into muscle memory. I do it hundreds of times a day, to the point where I actually have to open up AE and set a keyframe to remember what keys I use, because it's not a conscious thing any more. That's where you want to be.

Pro tip: at this point your layer has some animated properties. To show / hide all the animated properties for a layer, select it and press u. Boom. Bonus pro-tip: What I didn't know for the first few years of using AE (this is the 90s, so things were a bit hazy) was that double tapping it: uu will bring up all modified properties for that layer.



Ok, now hide the top layer. See that eye icon on the left of the top layer? Click that sucker. Annoyingly there is no kb shortcut for this by default.

Now go back to the start of your comp. Pop quiz: if end was the keyboard shortcut for going to the start, you win $1,000,000 cash money if you can guess the shortcut for going home to the beginning*.

With your bottom layer selected, adjust its scale rotation etc. so that it's to your liking, and set keyframes for the properties as necessary. Jump back to the end. You can use a new kb shortcut for this, one you should know: k. It jumps to the next keyframe, and j jumps to the previous keyframe. 

At the end of your comp, adjust the bottom layer so that it's how you want it. Because you have the stopwatches active for your transform properties any changes you make will now create a new keyframe. Look at me mum, I'm animating! If you scrub the timeline you'll see the magic happening, or if you want to watch it play in real-time (or whatever your machine can manage), hit 0 on your numeric keyboard, or ctrl0 on a laptop (from memory, might not be right). It will slowly play back as it renders the frames, then playback at something like real time once they're all cached (the green bar on the top of the timeline).

OK now for the parenting. On the right of the properties part of the timeline you'll see the parent column. And a curly icon called the pick-whip, or as someone once mondegreen-ed, the "pig-whip", which instantly became my preferred term for it. This will choose a parent for the layer. 



Note that there are (in recent versions of AE) pig-whips for all of the properties. This is for expressions (which is for another day, but they're awesome). Use the pig-whip on the top of the layer, not these ones or you'll get too confused. Also don't call it pig-whip if there's a client listening, you'll sound like an idiot.

We want to make the top layer the child of the bottom layer. At the end of your comp (this is important), use the pig-whip or the drop-down panel to set the parent for the top layer to the bottom layer.



What you'll see now if you go backwards down the time line is that the top layer will shrink in time with the bottom layer. Go back to the start and adjust any additional motion you want it to have. You may also want to set its opacity to 0 at the start, so that it fades in over the zoom.

Nearly done. There's One Weird Trick That Animators Don't Want You To Know that will sell this even better. Use Motion Blur. In the properties panel you'll see four columns of icons. If you can't see them hit f4. Click the one that looks like a stack of chips at a casino. Click it for both layers.



… Nothing changes … Ok, the reason that you don't see anything is that motion blur basically renders each frame a bunch of times at in-between positions and displays them all together. It's super computationally expensive, that's why it looks like casino chips**. So each frame might be rendered dozens, even hundreds of times depending on your settings. Hello slowness. 

To display motion blur you have to enable it for the layer, then enable it for previews. See the casino chips icon above the top right of the properties panel? Click that boi, and it should turn blue. Now you should see motion blur on any layer that has it turned on.



OK, save your project, jump back to premiere, and you should see the animation right there in your timeline, like it was all a crazy nightmare … or was it?

*cash money offer not valid in real life, terms and conditions apply, offer not applicable to residents outside Saint Kitts and Nevis.

**this is flat-out not true, but it helps me remember.