All my birds are cuddly tame or semi tame, which makes it a lot easier when they breed. They don't mind me feeding the babies or removing eggs for inspection, in fact I show them the incubator so they can see they're being looked after. Some people say pet birds won't breed, well that's wrong, mine do!
Believe me I've tried handfeeding from birth, with the special baby parrot food to precisely the right temperature in a dropper. But they always just let it dribble back out. Is there some technique to making them swallow? Do you have to tilt their heads back? I didn't want to make them choke. Once they have their eyes open, they seem more capable of swallowing by themselves and I just drop in some food each time they open their beak and ask for more.
I wish parrots were as easy to breed as cats. My pet cats bring up kittens all by themselves, and they're naturally cuddly, I don't have to hand feed at all!
First of all, as Itzjbean already told you, ANY TIME you allow your birds to breed, any time, regardless of the situation or any past situations and how they went, you MUST be ready to take-over hand-feeding the babies, and be ready with either a proper Brooder or a homemade Brooder that you can control and monitor the temperature in, as they must be kept in a temperature-controlled environment until ALL of their feathers have come in...Not just because they'll get physically chilled, but more-importantly because if they are physically too-cold, they will not properly digest anything that they eat, their crops will not empty between feedings, and they usually develop yeast infections in their crops and throughout their GI Tracts. So even if you don't have a proper Brooder (not an egg-incubator, a Brooder for the baby chicks), then you must have something set-up and ready to go BEFORE THE EGGS HATCH!!!
Here's a hand-feeding Primer I wrote, it's a 2-part, or 2-post Primer
Have you candled the single egg that was laid yet to see if it's fertile? Very easy to do, just hold it up in front of a flashlight and look for ANY veins. If you see even one red vein, it's a fertile egg. If within a week or so after the egg is laid you candle it and you see not one vein, only a yolk, then it's not a fertile egg, and you should put it in the freezer overnight, then you can take it out and put it back in the nest box and allow her to lay on it until she realizes that it's not going to hatch, and she gets bored with it and leaves it alone. At that point you can pitch it. Leaving an infertile egg in the nest box, if it's the only egg that has been laid, will keep your Grey from laying more eggs. OR, you can actually buy/order fake Grey eggs online or in pet shops, and swap the real, infertile egg out for the fake one, and then freeze the real one overnight and pitch it, then leave the fake one in the nest box to keep her from laying anymore until she gets bored with it and stops laying on it, then remove it from the nest box, AND THEN REMOVE THE NEST BOX SO SHE STOPS LAYING ANYMORE EGGS...
If you don't have a proper Brooder, the you must get a homemade one ready ASAP if you candle the egg and it's fertile, and you decide to allow it to hatch, as if your Grey decides to not lay on the chick, or to kick the chick out of the nest box, or to start hurting the chick, or to not feed the chick, you'll absolutely need to remove it immediately and put it in a Brooder of some type that is around 95 degrees F until the chick develops all of it's down undercoat, and then that is around 80-85 degrees F after their complete down is grown in and until all of their outer feathers are grown in, basically until they are ready to go into their weaning cage.
You can set-up a pretty basic Brooder by finding an adequately-sized cardboard box for a Grey chick, and then a large heating pad that has adjustable heating levels, an ambient thermometer, like the kind you use to tell the temperature outside and that you can hang in the back-half or affix to the side in the back-half of the cardboard box. Then you place the back-half of the cardboard box on top of the heating pad, and allow the front half of the box to be off of the heating pad. Then you'll cover the back-half of the box with a dark sheet, towel, or blanket, and this will create a warm zone and a cool zone for the chick to choose, along with providing the warm zone to be dark, as is necessary for young chicks. Then decide what bedding you want to use and put it in the bottom of the box, at least an inch of it. This not only helps with heat and comfort, but MOST IMPORTANTLY IT PREVENTS THE CHICK FROM DEVELOPING SPLAYED-LEGS...Get the Brooder to 95 degrees F in the back-half as read on the ambient thermometer, and mark down what temperature setting you have the heating pad on to get there, then turn it off. Then your emergency Brooder is all ready to go if necessary. THIS MUST BE DONE ANY TIME YOU ARE GOING TO ALLOW A FERTILE EGG TO HATCH, AND MUST BE DONE BEFORE THE FERTILE EGG IS SET TO HATCH SO YOU'RE READY IF YOU NEED TO REMOVE THE CHICK FROM THE NEST BOX...Just because your Grey took care of chicks during her prior clutch or clutches means NOTHING AT ALL.
BE READY, BE RESPONSIBLE, BE TOTALLY PREPARED BEFORE ANY EGG HATCHES. LONG BEFORE.
As far as being able to hand-feed/hand-raise a parrot chick, it's something that takes practice and is learned easiest from watching an experienced breeder/mentor, HOWEVER, once again, just like having a Brooder set-up and ready to go BEFORE any eggs hatch, IF YOU ARE GOING TO ALLOW ANY FERTILE EGGS TO HATCH, YOU ABSOLUTELY MUST BE PREPARED TO TAKE OVER HAND-FEEDING ANY CHICKS IN THE EVENT THAT YOUR GREY, FOR WHATEVER OF THE MANY REASONS SHE DECIDES NOT TO FEED THEM OR TO KICK THEM OUT OF THE BOX, OR STARTS HURTING THEM. THIS ISN'T OPTIONAL, YOU MUST AT LEAST HAVE ALL THE NECESSARY SUPPLIES AND BE READY TO GO!
You'll need to have a container of parrot hand-feeding formula on-hand, which you can buy at any Petco or Petsmart, and most independent pet shops that sell parrot supplies. Kaytee Exact hand-feeding formula is the most commonly sold formula, and does just fine. So always have a container of this on-hand BEFORE any eggs are allowed to hatch.
In addition to having the hand-feeding formula on-hand BEFORE any eggs hatch, you also must have a candy or cooking thermometer on-hand, which can be purchased for under $10 at any Walmart. You want one that has a probe that you can place into the formula, usually a metal rod-like probe. Digital cooking thermometers are best, I just recently bought a new one at Walmart for $9.97, it's a Taylor brand, is digital, and has a metal probe that folds-out. The formula that you feed a baby chick must be between 110 degrees F and 104 degrees F, THIS IS NOT OPTIONAL!!! ANY HOTTER THAN 110 DEGREES F AND YOU CAN BURN THE CHICK'S CROP AND CAUSE INFECTIONS, AND COLDER THAN 104 DEGREES F AND THE CHICK WILL NOT BE ABLE TO PROPERLY DIGEST THE FORMULA, THEIR CROPS WILL NOT EMPTY, AND THEY WILL DEVELOP FUNGAL (YEAST) INFECTIONS IN THEIR CROPS AND THROUGHOUT THEIR GI TRACTS...
****Another side-effect of feeding a chick hand-feeding formula that is not the correct temperature is that the chicks will literally refuse the formula and not eat it, often spitting it out or allowing it to dribble out of their mouths and down their chests (usually in this situation the formula is under 104 degrees F and is too cold). So this could have been one of your issues that was causing your chicks to not eat the formula properly...Either way, you must have a proper cooking thermometer and it must be in the bowl of formula the entire time you are feeding the chicks. Instead of reheating the formula constantly in the microwave, which can create "hot spots/pockets" in the formula that will burn the chick's, it's best to heat the water/unflavored Pedialyte in the microwave in a Pyrex measuring cup, and then adding the hot liquid to the hand-feeding formula. Then USING A WHISK, which is the best thing to use to mix the formula fully, vigorously mix the formula and then place the cooking thermometer in it.