This is a follow-on to this:
Why doesn't Superman make his own Flashpoint paradox to save Krypton?
That question asks why doesn't superman go back in time and do something to save Krypton or at least some Kryptonians from the doom.
Why doesn't Supergirl make her own Flashpoint paradox to save Krypton?
The motivations for Superman to not make a paradox, as enumerated in the answer to the previous question, include:
- Krypton's Red sun doesn't give the powers that a yellow sun does, so the super part goes away.
- Kryptonian Skepticism (aka super-resistant to being saved) makes them actively resist rescue attempts
- Time travel (nearly) always explodes badly/horribly/devastatingly
- A super-rigid morality on the part of the Kryptonian, such as Superman has, would disallow such actions.
While these are particularly true for Superman/Kal-El, there are some differences for Supergirl/Kara. Not only is she going to have stronger motivation to save Krypton, she is more likely to engage them in the face of their risk and complexity, and more likely to act if she thinks it is plausible.
- She is a lot more about the team than about a single individual. This means she is surrounded by people who are super-hero/best-on-the-planet in their own way that she leans on, and is challenged by. Her ability to think "outside the box" and rely on resources outside her own strengths is going to be substantially larger than her cousins. She is going to find alternatives to "blocked paths" that her cousin wouldn't. (Reason 1)
- She grew up there. Her biological parents died there. Every friend she had up to the day she was sent to earth, lived there and died there. She has roots there. She has people she loved and would very much like to save. Knowing it might be possible would be a compelling motive. She is also a product of that stubborn skepticism, and is likely to be more unrelenting even in the face of utter obliteration like they were. (Reason 2)
- She didn't grow up on earth in the same way he did. He has decades of fighting bad guys and seeing how bad the best laid plans go astray. She doesn't have a truckload of experience yelling "don't do it". (reason 3)
Risk-taking and bold action are more part of her character than they are for Kal-El's character.She has the impulsiveness and brave lack-of-wisdom endemic to youth to make her more likely to act. (reason 4)
Her exposure to the Flash is across genders, and in the show they seemed to have an attraction/tension that might lead her to make assumptions and take actions about parallel-universe travel and time-travel that are more risk taking and bold. Kara doesn't know what a time-wraith is. (Motivation)
- Her mind is more capable of nuance and complexity than his. He is very often "when you are a hammer every problem looks like a nail" while she is not. This means she is capable of considering, supporting, and executing more complex solutions to more nuanced and complex problems than he is. Consider her boss/mentor Cat Grant as a source of capability for this as well as Martian Manhunter (J'Onn) and her foster sister. (reason 1,3,4)
Disclaimer: I watch much more TV than read comics, so the Kara I know is from the TV show. (Arrowverse?) The superman I know comes from lots of cartoons, and a few TV shows since. If you have something to suggest from outside my limited experience, then I welcome it just as well as things from within my framework of understanding.