Since KA seems to be a lot smarter than a lot of us initially thought, I think it's useful to think through how this could have been planned and executed. I'm going to discuss two different scenarios: that MW's murder was in the works for an extended period of time (Scenario 1) and that MW's murder was a spur-of-the-moment decision (Scenario 2).
Scenario 1: KA has been plotting MW's murder for an extended period of time, perhaps months or even since CS's first instance of infidelity. Knowing that she wants to kill MW, KA plants an idea in CS's head that both of them should have weapons, maybe telling him that now that they are planning on traveling in the renovated trailer, they should have weapons to protect themselves if they are camping in isolated areas, so CS and KA go to a gun store and purchase 2 handguns. KA, knowing that she is going to need to flee as soon as she kills MW, starts considering what she would need to execute an escape plan. The most important things she needs to acquire are a fake passport, access to cash, and a place to go.
She goes on the dark web, or uses
one of the many Telegram channels specializing in the production of fake passports, to buy some sort of fake passport, most likely not a US passport. If she speaks French even passably, she may opt to purchase a Belgian or French passport as those are some of the easiest and most common ones passports to fake. She has been working in real estate and likely has access to some cash, let's assume $20,000. She spends $8-10,000 on the fake passport, which she gets shipped to a PO box, one of her rental properties, or the Wheelhouse Mobile business. While she is waiting for MW to arrive in Austin for the race, she withdraws additional cash from her banks
in increments of under $10,000 so it isn't flagged. She creates a 'go bag' which she stashes somewhere she doesn't believe CS will find it, such as one of the rental properties. Alternatively, she may give the bag to a family member/friend for safe-keeping and tells them she may need them to ship her the box at a later date. She may have even opened a PO box in NYC.
Then, when MW is in town and CS meets up with her, she kills MW. Detectives question and release her, and we know that she then went to a neighbor's house and frantically asked them to use their phone. Perhaps she asked the family member/friend to mail the box to the address in NYC. She then flies to LaGuardia, and has to wait there until the box with the fake passport, cash, and whatever else she might need to arrive before flying out of the country. Knowing that she would be receiving a package with the necessary supplies, she leaves Austin with only a yoga mat and few other things to not tip authorities off to her plan. Then she receives the package and pays cash and takes a cab to Newark-Liberty airport where she buys a ticket out of the country, perhaps to somewhere like Thailand or Vietnam. She uses the fake passport to get on the flight and gets out of the country.
Scenario 2: KA didn't have a long-standing plan to kill MW and it was a spur-of-the-moment decision. She confronts MW, shoots and kills her, and is brought in for questioning but is released. She now sees that she has time to flee and books a flight to NYC in an attempt to buy her more time to figure out her next move. She goes on the dark web and buys a passport (which probably wouldn't be possible as I highly, highly doubt she could obtain one in only 4 days), or pays someone who looks similar to her for their passport (more likely than buying a fake one). She spends four days in NYC figuring out how to acquire the resources and cash necessary to flee the country. Perhaps she reaches out to her family and asks them to purchase a passport for her/mail her one of theirs (if she has a relative who looks similar) or wire her money. Once she has a decent enough passport and some money, she takes a cab or Amtrak to Newark-Liberty, where she buys a ticket out of the country, boards the plane, and leaves.