In general, when young critters begin vomiting suddenly, my first couple of suspicions are that they caught something infectious (think stomach flu) or they ate something that did not agree with them. Both things can possibly pass on their own if given time, so I don't panic as long as they are still acting relatively OK.
It's likely the liquid you saw Milou vomit was what was left over after all the food in his stomach was gone. If he is vomiting everything that he takes in, I would hold off on giving him any food or water at all for at least a few hours to give his stomach time to settle. As long as his breathing is not labored and his gums are nice and pink and moist and he's acting relatively normally it's likely OK to continue monitoring him.
Kittens are notorious for eating strings and ribbons - if you have any suspicion that he has ingested a string, ribbon, or anything long and skinny like them, and he is continuing to vomit, this could be a life threatening emergency. If he is cooperative, you may be able to look under the base of his tongue - if you see any string stuck under there, this is an emergency, as he may have swallowed some string which could cause very severe problems. Still, though, the most likely causes of vomiting in young critters is either something infectious or something dietary.
After he's gone 6-8 hour without vomiting, I'd suggest offering him a small amount of water or ice chips (about 1/8 of a cup). If he drinks that and keeps it down for a couple of hours, you can repeat offering the water and also offer a teaspoon of food. As long as he doesn't begin to vomit again, you can continue to offer small amounts of food and water every couple of hours throughout the day. If the vomiting is continuing even after resting his system, then you should seek ER care.
If he hasn't had a full set of vaccinations, I would also have concern for a disease called panleukopenia, which causes severe vomiting and diarrhea. With panleukopenia, the symptoms likely will not let up at all and he can become dehydrated very quickly. If this is the case, then I would also suggest seeking ER care.
Please let me know if I can answer any other questions for you - and please forgive our delay in response tonight.