As indicated in Drifter196's answer, and in the comments above, the 616 version of Spider-Man does not have a degree in Chemical Engineering. As per What was Peter Parker’s college major?:
According to the Official Handbook of the Marvel Universe (Vol. 1 #10) Peter's major in college was Biophysics.
Currently, Parker has taken an indefinite leave of absence from the graduate program in biophysics at Empire State University, and has taken up full-time freelance photograph, primarily for The Daily Bugle,
... the Official Handbook of the Marvel Universe (Vol. 4 #2) indicates that his Doctoral studies are in Biochemistry
EDUCATION: College educated (science major), doctorate studies in biochemistry (incomplete)
In the Marvel-1610 continuity of the Ultimates universe, where Miles comes from, Peter was still a high-school student.
However, there are definite deviations in the Spider-verse film From Marvel-1610, including a blonde Peter Parker who's married Mary Jane, so we cannot really draw any conclusions from either Marvel-1610 or Marvel-616 comic book history. Given that the film's 1610 universe is so different, I think we have to take its statements at face value.
So, long story short, in all likelihood, in the Spider-verse 1610 universe, Peter Parker does have a chemical engineering degree.