They do not have rights to The Silamarillian, Unfinished Tales, or the other later books. The rights Amazon licensed are the same ones on the market since the 1970s that include The Hobbit and The Lord Of the Rings.
According to interviews, they combed through LOtR in particular and any lore mentioned in the text is fair game. Several chapters include some deep exposition (think about the Council of Elrod where they talk about Sauron and Isuldor, or discussing the history of Moria as they walked through the mines).
The books also include a number of songs that refer to the history of Middle Earth, as well as a huge exposition dump in the appendices to LOtR. Which is why we see ancestral Hobbits in the trailer, as there is an entire chapter of their history in addition to the background on Smegol in the text.
So if it was mentioned in passing in The Hobbit or the trilogy, it is fair game even if it is discussed in more detail somewhere else. But things like the Silamarills that are not in the books they have rights to are off limits.
The showrunners have said that within the limits that they have, anything that they fill in will not contradict anything else Tolkien has written.