As far as I know Kingo and CF-AUTO root are not compatible with the current time galaxy tab A. Any suggestions?
Side Note TWRP and CWM are not compatible with my device
When you say "TWRP and CWM are not compatible with my device", I reckon you didn't search hard enough, so here's something for you.
There are also brief steps in the thread. Basically just load up TWRP in Odin and flash a compatible SuperSU from there and you're good.
Do the root manually,
Google it to get more info, I will describe shallowly,
Get Odin, get bootloader, download bootloader into phone from download mode... (Do it through Odin)
From the bootloader, download root apps, or get Cyanogenmod so you can get root permissions by enabling developer options
Sorry for the vague answer, I am in a bit of a hurry, you can google it and trust me, you will get a lot of answers. Be careful, rooting will void your warranty and may brick your device.
Hope I helped,