So Hand-Axes are unfortunately not a Close Weapon so Flurrying with them is out upon first inspection.
You could have each of them receive the versatile design modification so that they may flurry, or a far out option is instead you go for Axe-Gauntlets*, does that fit the feel for what you are going for?
*They would need Exotic Weapon Proficiency
Slayer is the way to go for this. Ranger combat styles makes it easy to pick up two weapon fighting without have a sky high DEX. The Slayer also gives you much better out of combat utility, as well as studied target and sneak attack. Depending on if retraining is allowed you can have a solid build by 6th level. If retraining is not allowed the full build would not come online till 8th level.
1st Weapon Focus, Dazzling Display
2nd Ranger Combat Style: Two Weapon Fighting
3rd Power Attack
5th Hurtful
6th Ranger Combat Style: Two weapon Fighting
7th level Shatter Defense
8th level Combat Trick: Cornugun Smash
1st Weapon Focus, Dazzling Display
2nd Ranger Combat Style: Two Weapon Fighting
3rd Power Attack
5th Hurtful
6th Ranger Combat Style & retrain Hurtful to Cornugun Smash and the 4th level slayer talent to Shatter Defense.
When the build comes online your first attack allows you to get a free demoralize attempt. If it succeeds your foe is flat-footed to your attacks till the end of your next round. This allows you to apply your sneak attack damage to all your attacks.
The hooked axe has both the disarm and trip special weapon properties. It is an exotic weapon, but can be used as a martial weapon like a battleaxe without disarm/trip. EWP is easy enough to get... Half-Elf and Human can both start with it, but anyone with martial weapon proficiency can just buy proficiency for the price of a cracked ioun stone ( 1500gp). Humams can actually start with EWP twice, so you could start with proficiency in the Hooked Axe and the Tongi.
Something like Sliding Axe Throw could further add to your tripping nonsense... I mean utility... tripping utility. Being a TWF'er, you will probably have a high enough Dex to actually hit with the ranged attack, even with the penalty. Could even have a throwing axe in the off-hand, since it's light. Then throwing your axes could kind of just be standard practice.
2 throwing axes, TWF, blinkback belt, quick draw, haste item.
@ VoodistMonk
Could you give me an example build ?
Human with the Military Tradition alternative racial feature replacing their Bonus Feat, and Heart of the Fey replacing Skilled. Let's go with vanilla Slayer... at level one, just two-hand the Tongi since it has the better crit profile. From level two onward, TWF with a Throwing Axe in your off-hand.
1. EWP Hooked Axe
1. EWP Tongi
1. Quickdraw
2. RCS: TWF
3. Point Blank Shot
4. RT: Unbalancing Trick (Imp. Trip)
5. Sliding Axe Throw
6. RCS: Greater TWF
7. Great Trip
8. RT: Weapon Trick/Weapon Focus
9. Iron Will
10. RCS: Two-Weapon Rend
Probably put Weapon Focus on the off-hand Throwing Axe, to be honest. But you could easily grab Combat Trick for pretty much any combat feat you want. Wear Shifting Jerkin if you want the ability to change your Slayer Talents... which can be useful.
The build I recommended uses the early slayer talents to get the build working as soon as it can. The 10th level slayer talent will probably be used to pick up greater two weapon fighting. Underhanded Trick will give you improved dirty trick without needed to meet the prerequisites. Jaguar’s Pounce allows you to make a disarm or trip attack when you are dealing sneak attack damage, but requires Jaguar’s grace. Those may be worth taking the feat extra slayer talent to get once the build is online.
Another problem with the hooked axe is that it is not a light weapon. That means it has the same problems that using a battle axe would have. You end up with an extra -2 to hit on all attacks when using two weapon fighting. To me this is not a good choice of weapon.