Honestly, applying a strict definition of stream-of-consciousness will be difficult. Frankenstein is not written as a stream-of-consciousness. Rather, it is told in a series of nested narratives, in a common Gothic structure that builds on the epistolary novel structure. (This whole thing is supposedly told in letters back home.) What's more, the various narrators are pretty self-aware—far from stream-of-consciousness.
That said, the closest this comes to stream-of-consciousness is when Victor creates the monster in the lab, and when the monster is describing his preverbal state.
For information on stream-of-consciousness itself, see the link below.