"No 1099 was issued to the assistant, she was paid monthly in cash."

That payment type is fine. There are payment methods that are subject to 1099-K reporting rules (such as paying by Venmo or Credit Card = third party settlement entity) and those that are subject to 1099-NEC reporting rules (cash or check), and there are those that would have the person be on payroll, or be at risk of worker misclassification.

"Would IRS likely flag this as my client (the employer) should have paid by 1099?"

You don't pay "by" 1099. You can pay in cash, even for payroll (it's like cashing their takehome check, to hand them Cash and a paystub). What you have is a person not following any of the requirements. Yes, that's going to be suspicious, because there is a question right on the tax form regarding this topic. Have you examined the penalty for this? Is the assistant likely supposed to be a payroll employee?

Two wrongs won't make it right.