First - you need to find the sources for the kernel on the net. Then you need arm toolchain (arm gcc, etc). To compile kernel you need to do:
cp /boot/config-3.4.113-bananian ./.config
make ARCH=arm CROSS_COMPILE=arm-none-eabi-
the binary of the kernel should be in /usr/src/linux-kernel/arch/arm/boot/uImage or zImage. The DTB should be in /usr/src/linux-kernel/arch/arm/dts/*.dtb.
Then you need to find out which bootloader your system uses. If it is uboot you can use following command:
bootz 0x40008000 - 0x44000000
but first you need to load the kernel and DTB to memory from uboot level.
fatload mmc 0:1 0x40008000 zImage
fatload mmc 0:1 0x44000000 devicetree
If you are booting your system from MMC/SD card.