What is the best way to estimate next years taxes when you have uncertain capital gains interest and dividends?

Your estimate of your tax is only as good as your estimate of your income. There is no magic formula. You could use last year as a guide, or assume that December will be equal to the average of the last 3 months or 6 months. Basically you take your best guess.

there is a safe harbor that does not require you to estimate or even know your current year's income/taxes. for federal purposes, withholding and timely estimated tax payments must equal or exceed 100% of your prior year's federal tax. the 100% jumps to 110% if your prior year's adjusted gross income was $150K or more.

state laws vary. 

Q. What is the best way to estimate next years taxes when you have uncertain capital gains interest and dividends?

A. Opinions, on that, will vary. I recommend you use the download version of TurboTax, not the on line version. You can do an unlimited number of test returns. 

If you used the download version of TurboTax (TT), that is, you currently have TT 2023 on your computer, make a copy of your 2023 return (click file / save as). Name it something like "2024 Preliminary" and then replace your 2023 entries with your 2024 estimates. It won't be exact because the program uses 2023 tables and numbers. But, it should be close enough for most purposes. I use the override feature to change the standard deduction and MAGI numbers, on the forms, where appropriate. This doesn’t work with online TT, because you will override your 2023 return.

The Download TurboTax software also has a What-If Worksheet that you can use in forms mode to quickly and easily estimate your 2024 tax. It lets you copy the figures from your 2023 tax return, make adjustments as needed, and check a box to use 2024 tax rates. The What-If Worksheet does not affect your actual tax return.

Or you could Try this tool   https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1

Some Brokerages/Fund companies issue an expected year-end distribution amount for each of their Mutual Funds.  Then you can calculate an approximate final distribution amount yourself:

Fidelity has theirs on their website.  Both $$ already distributed up until December, and the estimated December year-end distributions on separate tabs, here:

Distributions by Fidelity Mutual Funds - Fidelity