What is your UC GPA capped weighted and fully weighted? https://rogerhub.com/gpa-calculator-uc/
Your SAT score is within range for all the UC’s, but with low acceptance rates for UCLA/UCB you should consider them a Reach.
As stated by @coolweather, there are a number of UC’s and Cal states beside UCB that offer Chemical Engineering. If you are leaning towards an Engineering major, for the majority of the UC’s and all the Cal states you need to get admitted as a direct admit.
Easier to change out of Engineering than change into Engineering. That said based on your uW GPA, your UC GPA capped weighted is around 4.1. Chemical Engineering will be very competitive so you need to apply widely. Here is some statistical data for the UC’s which is not major specific so expect any Engineering major to require higher stats and will have a lower admit rate.
Freshman admit rates for UC GPA of 3.80-4.19:
UCB: 12.6%
UCLA: 11.7%
UCSD: 38.7%
UCSB: 53.6%
UCD: 56.5%
UCI: 52.1%
UCSC: 75.7%
UCR: 90.1%
UCM: 96.1%
Freshman admit rates for UC GPA of 4.20 or above:
UCB: 42.7%
UCLA: 47.2%
UCSD: 84.2%
UCSB: 82.0%
UCD: 90.3%
UCI: 94.1%
UCSC: 92.7%
UCR: 97.5
UCM: 98.1%
2018 UC capped weighted GPA averages:
UCB: 4.23
UCLA: 4.23
UCSD: 4.16
UCSB: 4.13
UCI: 4.13
UCD: 4.11
UCSC: 3.96
UCR: 3.81
UCM: 3.71
2018 Data:
25th - 75th percentiles for SAT:
UCB: 1360-1540
UCLA: 1340-1540
UCSD: 1300-1520
UCSB: 1270-1500
UCD: 1220-1480
UCI: 1230-1490
UCSC: 1210-1450
UCR: 1130-1380
UCM: 1020-1280
Also do not dismiss the Cal States and they admit by your UC/CSU GPA capped weighted and test scores which determines your Eligibility index. (CSU GPA x800) + (SAT Math + EBRW).
Cal Poly SLO admits by MCA points which includes GPA, Test scores, HS course rigor and a small percentage of EC’s and major related job experience. If you want to know to calculate your MCA points, look at post #52 on this thread: http://talk.qa.collegeconfidential.com/cal-poly-san-luis-obispo/1694769-confused-about-mca-score.html
Best of luck and Cal Poly SLO is a great Engineering school even without Doctorate programs. There is nothing from keeping you in doing your Undergrad at SLO and then doing your Masters/PHD at a school like UCB.
So you are more interested in doing Research vs. working as an Engineering in the private sector?