I'm not sure specifically as there could be many different versions of such a fanfic. But generally, it might involve angels taking in Sam and Dean as kids and guiding them in a different way than in the original story, perhaps protecting them from other supernatural threats in a more angelic manner.
Writing a great adopt kid Sam and Dean fanfic requires a lot of elements. You should focus on character development. For Sam and Dean, show how they change and grow in the new family environment. For the adoptive family, show their journey of accepting the boys and all their quirks. The plot should be engaging. It can involve the boys' past catching up with them in the form of old enemies or secrets. Also, the dialogue is crucial. Make it sound natural for all the characters and use it to convey emotions and move the story forward.
Well, a common plot in such fanfics is that the adopted family discovers the boys' connection to the hunting world gradually. Maybe through some strange incidents that keep happening around Sam and Dean. Also, there could be a storyline where the family tries to give the boys a sense of stability and love that they never had before. This might involve family vacations and holiday traditions, all while the boys are secretly training to be better hunters in case they need to face the evil out there.
It could be Castiel. He's a very popular angel in the Supernatural universe and often has a connection with Sam and Dean, so he might be one of the angels to adopt them in the fanfic.
The fanfic 'angels adopt sam and dean' may have a plot where the angels see Sam and Dean as key players in a coming apocalypse or a major event in the supernatural realm. So, they take them under their wings. It could show the brothers learning new angelic magic or abilities. There may be a struggle between the angels' loyalty to heaven's commands and their growing attachment to Sam and Dean, which could lead to all kinds of interesting twists and turns in the story.
Well, it's hard to say for sure without reading the fanfic. But Castiel is a very common choice as he has been so closely associated with Sam and Dean in the original series. There could also be some lesser - known angels that the author has created specifically for this fanfic. Maybe an angel that represents a different aspect of angelic society, like an angel in charge of angelic education or something, who takes a special interest in Sam and Dean.
One common theme is loyalty. Dean and Sam are always loyal to each other in most of these fanfics, no matter what challenges they face. For example, in many stories, they will go to great lengths to save each other from danger.
Dean would probably be very protective. He's always been the big brother looking out for Sam, and with Sam as a kid, that instinct would be even stronger. He'd be constantly worried about Sam getting hurt and would keep him close at all times.