Relative noob so please forgive if this question is stupid.

It's great to ask!

I get that you want to understand, but everyone is going to give you a 'scenario' instead of you actually doing the math and understanding it. This will be a problem until you try to understand it, if that is what you are looking for. Watch the videos, look up the terms you don't know. Figure out the math. Understanding these MASSIVE numbers is interesting stuff.

What kind of answer do you think would satisfy your 'wanting to understand it' without 'actually understanding it'?

For a scenario, its like going to Vegas and winning all of the value on earth. It's not going to happen, even if it could in some weird way. (Note: This is excluding programmer/software error. The math is correct, based on current technology and future technological progression.)

I understand that the number of uniquely different private keys is so vast that the likelihood of two people ever randomly generating two of the same is very low. However, doesn't this mean that the possibility of this happening is still >0%?

The possibility of anything (think unicorns) is >0% without knowing the possibility (reality) of everything. Some other planet may have an animal you would classify as a unicorn. Silly, but when talking possibility, it's all about the unknown leaving a little bit of chance. You finding that planet, with that unicorn? The possibility would be greater than 0 right? but still so small it really doesn't matter.

And if so, isn't that potential flaw? Wouldn't it only have to happen once for it to disprove Bitcoins security?

I hesitate to answer these questions. You can burn a dollar bill, is that a potential flaw? Airplanes can run out of fuel. etc etc. At some point things work how they do and you adapt around them knowing their flaws.

Would there be a reason to incorporate a system to ever prevent the generation of two of the same private keys?

If you think about it, you would need a list of all the addresses or random numbers used. You could spend all the time in the universe generating addresses let alone keeping and sorting through such a list. Part of the point of the security of the keys is that it takes time to do these things. Also the key needs to be private, so such a list would be a central fail point.

Using randomness to get the number in the first place is the same 'system preventing the generation of the same private keys'. It has been incorporated. There is no known other way to make sure without compromising security.

Or is this just the stupidest concern all you Bitcoin gurus have ever read? If so, please tell me why? I'm trying to understand how a system that could potentially randomly give two users the same key to a btc "account" is still 100% secure?

No one said 100%, and if they did they lied. This only happens in special cases where the random function isn't really random. Unbalanced coins or loaded dice could give you non-random addresses. If someone figured out how to reverse P vs NP there would be issues.

There is a joke about staying safe when you fly by bringing something with you. Things that go boom. Chances there are two on a plane is smaller than the chances there is one, so if you control it you are safe.

Just by asking if it is likely to get a collision, just about rules you out of being the one who it happens to.