Rek'Sai excels in the jungle best because of her built in health regen from her passive (Fury of the Xer'Sai). Start off by buying a Hunter's Machete, two Health Potions, and a Warding Totem. This would be the standard build for all junglers. Start off by leveling Queen's Wrath/Prey Seeker. Begin wherever the bottom lane is. Ex: If you are on red side, start Gromp; If you are on blue side, start Krugs. Since Rek'Sai doesn't use mana, you can start either. In the case that you are on blue side, start the Krugs by smiting the Krug as soon as they spawn. This will cause you to gain the buff given by the Krugs and allow you to start stunning every 5 basic attacks. Activate Queen's Wrath when they spawn to do AOE damage and activate it again whenever available. After finishing Krugs, level up your Burrow/Unburrow. Burrow immediately after finishing any jungle camp. You will build up Fury from Fury of the Xer'Sai. Fury can be consumed when Rek'Sai has less than 100% health. Fury is turned into health when Rek'Sai is burrowed. Burrow as soon as you leave a jungle camp and upon starting a new jungle camp, place yourself directly in the center and use Unburrow. This will knock up the entire jungle camp. Upon becoming Unburrowed, use Queen's Wrath to start doing AOE damage to the entire jungle camp. A small purple/red circle will be around the unit that was recently knocked up by Unburrow. During the time that the circle remains there, the unit cannot be knocked up again by Unburrow. When the circle is gone, Burrow and instantly Unburrow again to knock up the camp. This is especially useful when killing buffs because they take longer to kill. After clearing Krugs, then Red Buff, Burrow, and go directly to Gromp. By this time, your smite will have came back up. Use Prey Seeker on the Gromp before it is in vision and then Smite it. Move in and use Unburrow to knock up the Gromp and use the strategy mentioned above to kill it. After killing Gromp, you will level up Furious Bite/Tunnel. After killing Gromp and using Burrow, move onto the Blue Buff. Unburrow and knock up the camp. Activate Queen's Wrath like normal. When attacking camps at this point, use Furious Bite when your Fury Bar is full. Doing this will cause Furious Bite to deal additional true damage to the target. Use Furious Bite to act as a miniature smite, so use it against the larger monsters in the jungle camps. Once you finish Blue Buff, move onto Wolves, and then Raptors. Note, that if you at any point are low on health while clearing, use the two Health Potions from before. Use Tunnel to move faster between jungle camps. After leveling it, you can start making a tunnel system through your jungle that allows you to clear faster by eliminating the time taken to move from jungle camp to jungle camp.

To recap:
Clear camps by moving in Burrowed, then Unburrow and turn on Queen's Wrath. When basic attacks and Queen's Wrath fills up your fury bar, use Furious Bite to deal extra true damage. Prey Seeker can be used to deal a little extra damage before starting a camp or to gain vision for a long-range smite. Use Tunnel to move between jungle camps quicker.