Long story short, I used to occasionally run Jungleona, but then they buffed the camps, and I couldn't do it anymore. But now they've nerfed some of the camps a little and added Bami's Cinder to the game.

The Cinder was probably intended to help junglers like Sejuani who have trouble with early-to-mid-game clear speed. But Leona got a boost too. I used to get an early Vampiric Scepter into an eventual Blade of the Ruined King just because the build path for Sunfire Aegis used to be impractical - zero DPS until completion (chain vest + giant's belt).

The Cinder is a lot more affordable. You very well might be buying it on your second recall - easily so if you have a successful gank or two. Once you have this item, your clears become sort of slow instead of plain horrible.

This is an adventuresome build. It can be fun to break the meta, but you will want to give it the most serious effort you can manage. You will need a team-queue, or you can try it in Team Builder. Ranked 1s or 2s will invite occasional skepticism and drama.

- First clear is very bad. Later clears are fairly slow.

+ Ganks are pretty awesome

- Almost no clean-up power if your lane gets totally wiped out (Blade of the Ruined King is about the only item that even lets you clean up just a little bit, and it's mostly not worth it)

+ Become a very stubborn immovable object late-game with the extra gold

- Objective control is necessarily team-oriented. Steals will be smite-flash only, for the most part.

A lot of the negatives are ultimately due to having a chunk of her damage locked in her passive. The trade-off might be worth it if you have tons of damage on the rest of your team, or if you're running a protect-the-hypercarry team comp. The upside is that if you really want to run a disengage support, you can!

I want to test this more, but preliminary tests of the basic camp clearing makes this look like an adequate choice to me. I have also heard reports that Jungleona is a thing that has been done, just not in actual LCS matches. It may be too risky for pro teams to go for, but it wouldn't be the first unconventional pick to do well, either. If possible, group at 1 and avoid 1v1 whenever you can. With a good team, some wards, and some pings, you shouldn't ever be totally alone.

Gromp, then wolves, then wraiths. Then you might want to gank a lane if there's a good option available. You can go on to mini-golems if you want, but only if you know FOR SURE that the enemy jungler won't be there for an easy kill. You will probably get very low on health doing this.

When you do Gromp, you can hold your Smite until the end if you have a lot of help, or you can smite right away for the poison damage if not.

Also, if you can arrange a double jungle start, this could help a lot. Probably with a top laner who will help with a few camps before teleporting top. This might not be something you can really arrange in solo queue, though. You should probably tank the monsters, because you can Smite the red buff for a heal-up.

Attack damage marks - Since Machete applies a DoT these days, AS doesn't scale. Flat AD it is for the first clear power.
Flat armor marks for the early clear.
Scaling CDR glyphs for the late game. Optional substitutions are available, such as scaling MR. But CDR is a strong stat.
HP5 quints for the first clear especially.

For Masteries, straightforward 5/25 (or 6/24 if you want more CDR) will do it. See notes if you want to. Perseverance is very important.

Leona has so much bonus resists on W that it makes sense to be health-heavy. The effective health scaling of W's stats with health is a little stronger than W's % scaling off of bonus resists, at least for early items. At any rate, Bami's Cinder is mandatory early. Health Potions and/or Rejuvenation Beads can help you endure the first clear or two. With Mobility Boots and Emberhulk-Chilling Smite, you have everything you need to gank as well as clear camps adequately.

Warden's Mail is just a good armor item, and you need one. Sunfire Aegis is no longer an option with Emberhulk, and there is no alternative to Emberhulk worth getting. Note that Randuin's Omen's active scales with current resists, which means you should have W active when you use it.

Warmog's Armor can be nice if you're nearly unkillable, but it's a waste and unlikely to help much if you can't live through fights anyway. It's a very swing-dependent item.

Spirit Visage has a good mix of stats, but the unique passive is best when stacked with Warmog's, and under similar circumstances. You can consider other CDR and MR items instead if you want.

Guardian Angel isn't bad, but I like health better early on. If you have enough experience with GA to know exactly when it'll ruin your enemy's day, then go for it.

CDR is my favorite luxury stat on this champion. It allows for frequent re-engaging. It just isn't worth getting Ionain boots over. I prefer Mobility Boots for avoiding poke and making catches, followed by either defensive boot situationally.

You can push a side lane with Cinderhulk, which even a support Leona with Sunfire Aegis could do anyway. But you can complete this item much faster than a support could safely get Sunfire Aegis, if ever. You can nuke a wave with W and Cinderhulk, and you can even throw an ult in there too if you're confident in your vision and the game tempo that you won't miss it - you wouldn't be the only champ to ever do so, and it's not wrong here either, in the absence of a better gold sponge.

It's up to you and the game's tempo exactly how many jungle camps you want to clear, but you can and should do them frequently. Wraiths and Wolves become adequately fast after Bami's Cinder. Mini-golems might be the worst, while Red and Blue are good to give away regardless. Arguably, Red buff isn't wasted on her, but it's not ideal either.

You might want to pick up a Sightstone and switch your trinket to a sweeper. This is your call. If you play on a very vision-focused team competitively, then you might make it pay off. I love my tank stats, though.

Other than that, she's still Leona, just bigger and badder. Enjoy the extra stats, and have fun bending the meta.