Android - After flashing TWRP with Odin, nothing happens and the OEM recovery is still there

Before you flash the recovery, untick the Auto Reboot option in ODIN. Then flash the recovery. After flashing in done, reboot your device directly to recovery mode from download mode by pressing Vol up + Power + Home button together. Now you will see the TWRP recovery is booted in your device. Now you can reboot normally and your TWRP will be installed.

Per this page,

WARNING: Do not boot into Samsung's ROM without first applying our Root .zip. Samsung's OTA updates install /system/etc/install-recovery.sh and /system/recovery-from-boot.p, which cause Samsung's ROM to replace the recovery image you had just flashed with the stock recovery. Our Root .zip removes these files, thus preserving your custom recovery. Follow the directions below to boot directly into CWM recovery.

Which is good information because it's telling you exactly what happening. However, you can get around this without downloading their questionable files: After you install the TWRP Recovery with Odin the device will reboot. After it vibrates in the rebooting process, pull the battery. Have it ready to pull, it boots fast.

Pop the battery back back in, and hold your recovery sequence (Vol Up+Home+Power). This will get you into the TWRP, and you can now sideload, or if that fails adb push $file /data/ the files you want to install.