Yes, it’s grammatically correct to repeat the word “from”, like this:
Here’s the formal definition from the ABC Institute from their book The World’s Best-Loved Formal Definitions: …
However, as you probably guessed, it sounds a little clumsy. English provides many alternative ways to say the same thing. Here are a few examples:
Here’s the ABC Institute’s formal definition from their book De Ratione Definiendi Æquivocando: …
Here’s the formal definition from the ABC Institute, found in their book From Genus, From Differentia: …
Quoting A Child’s First Book of Definitions, here’s the ABC Institute’s formal definition: …
More generally, here’s how to think up alternatives to fix a repeated or unclear preposition: (1) see if you can use the possessive case; (2) think of something more specific to say in place of the preposition. As the examples of “found” and “quoting” illustrate, the new word will often be a verb. That suggests another strategy: (3) think of a verb.