Do I have to account for 1099-DIV if it's a custodial account for my kids?

[Hal_Al]

It depends on the amount.  If the total income (usually boxes 1a + 2a) on the 1099-DIV,  is less than $1100 and that is the child's only income, it does not need to be filed.  (The amount shown in box 1b is already included in box 1a and should not be counted again.)

You do not  report his/her income on your return (see exception below). If it has to be reported, at all, it goes on his own return. If your dependent child is under age 19 (or under 24 if a full time student), he or she must file a tax return for 2021 if he had any of the following:

1.          Total income (wages, salaries, taxable scholarship etc.) of more than $12,550 (2021).
2.          Unearned income (interest, dividends, capital gains, unemployment) of more than $1100.
3.          Unearned income over $350 and gross income of more than $1100
4.          Household employee income (e.g. baby sitting, lawn mowing) over $2100 ($12,400 if under age 18)
5.          Other self employment income over $432, including money on a form 1099-NEC

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.

If his only income is from interest and dividends, Alaska PFD or capital gains distributions shown on a 1099-DIV, there is a provision for entering it on your return, using form 8814. Enter at Less common income / Child's income. But, it is usually best for him to file a separate return, as qualified dividends and capital gain distributions could be taxed at a higher rate on the parent's return. 

[HelenC12]

It depends what the dollar amount of dividends your child received. 

The rules change when your child receives income from sources other than employment, such as interest and dividend payments. When the 2021 total of this type of income exceeds $1,100, then a return must be filed for your child.

If your child’s unearned income only consists of interest and dividends, then you can elect to include it on your own return and combine it with your income. Do this by completing IRS Form 8814 and attaching it to your personal tax return (TurboTax will do this for you).

However, depending on the level of your income, making this election may result in higher income tax than if you prepare a separate return for your child. This is because it could push you into a higher tax bracket, where higher tax rates may apply. If you decide to prepare a separate return for your child, the same reduced standard deduction rules detailed above will apply.