Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am very sorry to hear about Romeo's vomiting after eating greasy chicken.
Vomiting/retching in a younger dog can be from several causes. Common ones are a quick change in diet, or eating something unusual or fatty, too many treats, especially fatty or spicy treats, eatings things they should not such as things found in the yard, toy pieces or garbage, viral or bacterial or parasitic infections.
More serious causes include pancreatitis, esophageal reflux, a dietary allergy or sensitivity, inflammatory bowel disease, internal organ failure (kidney or liver disease), a full or partial gastrointestinal obstruction or even infiltrative cancers such as lymphoma (not likely at his young age).
At this point we can try some things at home because we know that he was fed something fatty and unusual, but he may need to see a veterinarian if he isn't coming along well.
To try and settle his stomach now you can try either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These will reduce stomach acid and should help if this is related to simple nausea and gastrointestinal irritation from eating something he should not have. They can be given for several days.
I would not feed him any food for 24 hours even after the acid reducers are started.
This should help stop gut spasms and restore normal gut motility.
Starting a couple hours after the acid reducers small amounts of water or ice cubes given frequently are fine as he needs fluids after all that he has lost with vomiting.
You can give him pedialyte to replace electrolytes too but Gatorade is much too high in sugar which can make intestinal irritation worse.
If things are going well after his food fast and the acid reducers start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken), all fats drained off the meat, mixed with 2/3 boiled, plain white rice. Feed several small meals a day. Once he feels better (no vomiting for 48 to 72 hours) start mixing in his regular dog food very slowly. Less bland more regular with each day. It should take a week or so to convert him back.
If Romeo is continuing to vomit and is feeling poorly though, especially if he isn't current on his vaccines, it would be best that he see a veterinarian now as anything you give him orally will just come back up worsening his dehydration.
If he has a tense painful abdomen, becomes very lethargic, begins vomiting again or runs a fever greater than 103.5F then he really must be seen by a veterinarian as soon as possible.
Best of luck with your little one, please let me know should you have any further questions.