For what it's worth 8 months later, I was able to use PyOCD and the the built-in debugger on RT1064-EVK board to flash the Zephyr blinky program using MCUXpresso's flash programmer. Thus avoiding (for now) the need to buy a J-link probe. I didn't need to change much of anything.
What I did was use the MCUX option to save the flash command it uses to a file, and then tweaked the file so it's a script I can pass in whatever elf file I want:
$MCUX_IDE_BIN/crt_emu_cm_redlink --flash-load-exec $1 -p MIMXRT1064xxxxA --flash-driver MIMXRT1064.cfx -x $HOME/bin --flash-dir $MCUX_FLASH_DIR0 --flash-dir $MCUX_FLASH_DIR1
(some of that stuff may be unnecessary)
I copied MIMXRT1064xxxxA_part.xml and MIMXRT1064xxxxA.xml from an MCUX project directory into ~/bin (hence the -x $HOME/bin in the command above)
The script will flash the build/zephyr/zephyr.elf no problem. I didn't have to change any jumpers on the RT1064-EVK other than to set SW7 to boot from internal flash. I didn't have to change anything about how the zephyr sample program is built.