If you want to flash custom ROM on your Samsung Galaxy Tab 3 10.1, you will need to download CWM (clockwork mod) recovery on it. After that, you would not only be able to flash custom ROMs, but also root it.
Get Odin here: Odin3.07
Get your Tab in DOWNLOAD mode, and connect to your PC
Open Odin, and click on PDA to select the recovery you want to flash
Click START and wait till it’s finished
Reboot, and check if the recovery is flashed
PS: If something goes wrong, and you want to roll back, you can download stock recovery from here. Follow the same steps as above.