How would I complete CTR for an individual doing business as where the business is not using the individual’s social security number?

They should not be. A sole proprietor's EIN is only used for IRS and payroll purposes and not banking.

So file CTR with Part 1 listing the individual and dba’s name in item 8?

Yes. Use the SSN of the owner and include the DBA name of the business (if one is used) in item 8.

John Doe deposited $10k cash into John Doe DBA Flower Shop. John Doe also deposited $2000 into his personal checking.

Would this only require one Part 1 listing John Doe and $12,000 cash as conducting on own behalf?

Yes, one part 1 listing (John and Flower Shop are one and the same "person"). Include the DBA name in item 8. Check item 2a and item 3. List both deposit accounts on part 1.