Can I get a copy of 2019 taxes, if my ex-husband won't give me a copy. We were still married last year. He filed for us jointly.

You can get a copy from the IRS, see Welcome to Get Transcript.

he would need to grant you access to his TurboTax account - account, user name, and password - seems unlikely since he won't give you a copy. however, you can get a copy from the IRS 

Request Online
What You Need
To register and use this service, you need:

your SSN, date of birth, filing status and mailing address from the latest tax return,
access to your email account,
your personal account number from a credit card, mortgage, home equity loan, home equity line of credit or car loan, and
a mobile phone linked to your name (for faster registration) or ability to receive an activation code by mail.
What You Get
All transcript types are available online
View, print or download your transcript
Username and password to return later

You want a tax return transcript.

Tax Return Transcript - shows most line items including your adjusted gross income (AGI) from your original Form 1040-series tax return as filed, along with any forms and schedules. It doesn't show changes made after you filed your original return. This transcript is only available for the current tax year and returns processed during the prior three years. A tax return transcript usually meets the needs of lending institutions offering mortgages and student loans. Note: the secondary spouse on a joint return must use Get Transcript Online or Form 4506-T to request this transcript type. When using Get Transcript by Mail or phone, the primary taxpayer on the return must make the request.

Also, use 4506-T if you do not have everything needed to register to get a copy online

https://www.irs.gov/pub/irs-pdf/f4506t.pdf