uboot has command "mmc dev [dev] [part]"
From your log, MMC: FSL_SDHC: 1, FSL_SDHC: 2
mmc dev 1 switches to SDHC 1
mmc dev 2 switches to SDHC 2
Because SDHC2 is emmc, you can
mmc dev 2 1 switches to emmc boot partition 1
mmc dev 2 3 switches to emmc boot partition 2
mmc dev 3 3 switches to emmc use partition.
Because the emmc boot partition is small you need to switch to use partition and flash the image.
But in the binary demo image, NXP doesn't provide the script to flash image to the emmc use partition. You need to write down by yourself, using such as uuu download command..., etc. Manually flash the image to use partition.
But after that, you also need to switch to boot from use patition, using mmc partconf
mmc partconf 2 0 7 0. Note 7 is enable use partition to boot.
Another way, you can change the uboot configuration. Remove some no necessary module/configuration for your project to make the flash.bin smaller can fit the 2M emmc boot partition.
Maybe remove the spi, ethernet ..., etc.