Background: I have been interested in making a flash app for my TI-89 Titanium just to learn more about how the process works and what all is going on (Electrical Engineering taking classes such as Microprocessors). I am hoping to make a small sample app in assembly and maybe another one in C.
Question: I have not been able to find resources on how to structure, assemble, build, and debug a flash app for this calculator. Could any one help me with this?
I can do the assembly, I just need resources on how to piece it together and get it installed on the calculator.

You'll want gcc4ti (or the AFAIK-no-longer-maintained TIGCC). There is/was an official TI SDK for the 68k calculators as well, but I can't find it on their website now.

Nobody really writes (or, wrote) anything but C for the 68k calcs as far as I know. It's unnecessary work because 68k is just a good machine for compiling C to. Have a look at the examples that come with gcc4ti for a starting point. If you really want to try writing assembly, you're probably best off looking at what kind of code the compiler emits and emulating that.

Thanks! Do you know how to compile the code into a flash app? Also, the debugging with TiEmu, how do I input keypresses as I am debugging/attach to the specific flash app?

Unless things have changed substantially over the last few years, unfortunately nobody ever bothered to write a linker for TIGCC/gcc4ti that could create a flash application. It's a pipedream of mine that perhaps one day someone will write a proper flash app linker for the 89; someone includes me, assuming I ever find the time to make it happen.

There *have* been one or two community-made flash apps that used some combination of the old TI official SDK to link and gcc4ti/tigcc to build; GTC was one of them.

The software you would want is called "TI Flash Studio" if you can find it somewhere on the internet; unfortunately it was written using Microsoft's old Java platform, which makes it doubly difficult to get running on any kind of modern system since you'd need to acquire a copy of that as well.

You haven't listed any reason why you'd absolutely need to make a FlashApp, rather than an ASM program

On the TI-68k series, FlashApps have never been popular, because of at least three reasons:
* the toolchain sucks, to begin with. The TIFS IDE is slow and buggy, the embedded emulator is a joke, and the C compiler is buggy and often generates bad code;
* FlashApps needed (free of charge) signing by TI. At some point, AFAWCT, they quit responding to signing requests. The factoring of the public (validation) RSA keys, in 2009, made the community able to sign FlashApps on its own. However, by then, TI-68k programming in native code languages was already pretty much dead: the community belittled in 2006-2007 and never grew back up;
* on the TI-68k series, ASM programs have few annoying restrictions, unlike on the TI-Z80 series (which have less RAM and a small addressing space to begin with, so executing from Flash directly makes far more sense). Though TI instated an artificial restriction on the size of ASM programs and Exec strings in AMS 2.xx, it is laughably easy to work around, and it was effectively disabled by TI on the 89T.
ASM programs can do almost everything users and programmers need, including full-blown event-driven programs (not popular, but possible), a number of event hooks, various RAM-resident programs for expanding functionality (so-called "kernels").

FlashApps are the recommended way to perform deep OS integration, the likes of making your own language localizations, or providing multiple TI-Basic extensions in the namespace of the FlashApp. They execute from Flash, so they take less RAM when they're executing.
But I strongly doubt you need or want to do deep OS integration, and there's usually plenty of RAM... As such, I'd simply recommend making ASM programs

GCC4TI has more features, more optimizations and fewer bugs than the dead TIGCC. Of course, I'm biased, but I'm nevertheless stating facts

Thank you all so much for the information!
I found a torrent with the SDK in it, but it does not seem to have any seeders. Do any of y'all have the SDK & documentation? I could run it on an XP virtual machine possibly.
@Lionel Debroux there really is no practical reason for me wanting to make a flash app. I have just always wanted to ever since I learned how to make programs in BASIC on my old TI-84 around 8 years ago. That's what go me started programming. Since I am finally learning assembly, I figured it is finally my chance to do a small proof of concept flash app.

On the TI-Z80 series, you should indeed make a FlashApp, though assembly programs can the job do for small stuff.
But on the TI-68k series, frankly... making FlashApps is being a glutton for punishment

Well that's no good. I'm not even sure where my 84 is anymore because I only ever use the 89. It has so much more functionality. It's kind of sad that it seems to be forgotten; most all of us engineers use them.

Indeed, the 89 has much more functionality. But for your purposes, I really advise just making an ASM program with GCC4TI, like nearly everyone else did since the dawn of the TI-68k series on the older TI-92 (after Fargo was invented, at some point between 1995 and 1997), before the 89 / 92+ models grew Flash memory and later FlashApp support with AMS 2.xx in 1999

On the TI-Z80 series with Flash memory support, FlashApps are much more popular than ASM programs; on the TI-68k series, ASM programs are much more popular than FlashApps.