This one shocks me with its longevity. Truly, if this worked, there would be no market for birth control. But this idea lingers, so let's talk about it.
The vagina is like a self-cleaning oven...there is no need to use external cleansers for any reason, nor should you. There is a balance of bacteria in the vagina that protect it, and disturbing that balance is quite unpleasant. Have you ever contracted a vaginal yeast infection after taking antibiotics for strep throat, for example? This happens often.
Putting what amounts to food in your vagina is even worse. Not only does the carbonation aggravate the vaginal tissue, it provides food for bacteria, perhaps the wrong bacteria. And, in the end, it does not accomplish the goal of preventing pregnancy.
The cervix provides a very effective barrier between the vagina and the uterus. It secretes protective mucus, and it is tightly closed except during ovulation when it opens slightly to allow sperm to enter. The mucus strips out everything from the ejaculate except the sperm, which is critical because prostaglandins in the seminal fluid could cause shock if they got into the uterus.
And therein lies the reason a douche doesn't work after sex. Sure, you might wash out any sperm in the vagina, but that is not the sperm you want to eliminate--the sperm that has already made it past the cervix is high-tailing it to the the fallopian tubes, out of reach. Think you can be quicker than the sperm? Not unless you keep a soda by the bed, ready to use within seconds, and even then, you underestimate the speed of the ejaculation.
Think some more about how silly this idea is. Why do you need a soda douche if fluids could so easily get into the uterus? Couldn't you just go swimmimg or take a bath? Those ideas don't work, and neither does using a bidet.
Take a pass on this idea if you truly want to prevent pregnancy. If you are strapped for cash and can't afford birth control, visit a public health clinic or abstain because a douche of any kind will not do the job.