I'm not specifically familiar with your state software. The following is a "generic" answer.
There is no federal deduction for making a contribution to a 529 plan. Some states allow a deduction on the state return. If your state is one, it will come up in the state interview; usually in the "Here's how (your state) handles income differently" section.
To enter your Section 529 Brightstart contributions in the Illinois portion of TurboTax:
Open TurboTax Online
Select Tax Home in the left pane
On the Hi, let's keep working on your taxes! screen, select the dropdown on the right side of State Taxes, then select Start, Continue or Pick up where you left off
Select Prepare State in the left pane
Work through the next screens until you reach the Status of your state returns screen
Select Start or Continue to the right of Illinois
Work through the next screens until you reach the Here's the income that Illinois handles differently screen
Select the dropdown to the right of Education: College savings, ABLE accounts, and student loan repayments
Select Start to the right of College savings and prepaid tuition plan contributions.
Enter all relevant information in subsequent screens
This is where you'll enter information when you've contributed money to a college savings pool or pre-paid tuition program, including Bright Start and Bright Directions college savings pools, and College Illinois pre-paid tuition programs.