I am sorry to hear you are worried about Kitty. I am a veterinarian and will do my best to help. My name is Rebecca.
How long has she been vomiting, and having diarrhea? Is she able eat and drink and hold anything down, or does everything that she takes in come back up?
Coconut oil has many benefits, but won't keep fleas off of her. It could cause diarrhea.
There are many things that could make a kitten vomit and have diarrhea: infections, parasites, eating something that disagreed, eating something like a string or yarn or a toy that is causing a blockage in her intestines. Has she had any vaccinations? Feline distemper can cause vomiting, diarrhea, dehydration and even can be fatal, but if she has had vaccinations she should be protected from distemper.
If I could, I would begin by examining her: Check to see if her gums are pink (if they look pale, that can be a sign of something serious), take her temperature with a rectal thermometer (normal is between 101 and 102), feel her lymph nodes and palpate her internal organs, listen to her heart and lungs, feel the quality of her pulses. I would also check a sample of her stool microscopically for parasites and infection. If she can't hold even water down, and keeps on vomiting, she should see a veterinarian.
You can start by not feeding her, and offering clear fluids (water, broth, Pedialyte) in small amounts. If she can keep liquids down, then after 4 to 6 hours, try a tiny bit of food. The big problem with vomiting and diarrhea, so try to get her to take small amounts of liquid often. If she won't take liquids, or vomits them back up, she needs to see a veterinarian.
You can try giving her famotidine (Pepcid AC) for vomiting, at 1/4th of a 10 mg pill twice daily. Giving her probiotics, beneficial bacteria supplements may help, if she will take some food. I like the probiotics made just for cats like Fortiflora or Proviable.
Let me know what else I can answer or help with, and how she is doing. Kindly consider rating my answer (always appreciated!); you can still get back to me with questions and updates after rating. Rebecca