Way of the Leaf:
Way of the Leaf monks train themselves to understand the flow of battle and move with it rather than face it head on. This style focuses heavily on evasiveness and redirecting your enimies actions against them.
Redirection
Lvl 3: You gain Reactions per round equal to 1/2 your Dex Modifier (Rounded Down) in addition to the 1 standard Reaction. While Dodging, if a creature misses an Attack Roll against you, you can use a reaction to redirect the attack to hit any creature within 5 feet of yourself including the Attacker. The target of the redirected attack takes half damage.
You also gain the ability to expend Ki to make a reaction equal to 1+1 per Ki expended this way this round.
Leaf Step
Lvl 6: When you are subjected to a Dexterity saving throw or a contest where you make a Dexterity contest you can use a reaction to attempt to move out of the way, moving up to 10 feet (15 feet if you are dodging). This movement is not impeeded while moving through a space with occupied my a hostile creature. If this movement moves you out of range or out of the area of effect of the ability.
Be the Leaf
Lvl 11: You become like the Leaf. You can take the dodge action as a bonus action. When targeted by an opportunity attack, add half you Dex mod to AC until the attack is resolved. You can also use reactions while suprised and even while you are unconcious you are able to make 1 reaction per round.
Leaf on the Wind
Lvl 17: Your reactions per are now equal to you Dex Modifier. The damage from Redirected attacks is no longer halved. When you are targeted by oppirtunity attacks add your Dex mod to your AC. Once per Short Rest you can force 1 attack to miss you.
Meanwhile the rest of the features are... rather weak.
StarTwister - Love the premise and where you are going with this. I love the idea that this style encourages the PC to use the Dodge action every turn, but as Yunru mentioned there are some balance issues. Monks fuel most of their features of Ki, so I think the solution is to increase the importance of that and to tie the reactions to Prof bonus instead of Dex. Below is how I would rework if I were bringing this concept into my campaign.
Redirection - Lvl 3 You can spend 1 Ki point to gain an additional reaction. You can do this a number of times per round equal to your prof bonus. While Dodging, if a creature misses an Attack Roll against you, you can use a reaction to redirect the attack to hit any creature within 5 feet of yourself including the Attacker. The target of the redirected attack takes half damage.
Leaf Step - Lvl 6 When an opponents attack misses you, you can use a reaction to teleport to a square you can see within 30'.
Be the Leaf - Lvl 11 You can take the dodge action as a bonus action. You automatically take the dodge action when surprised. Once per short rest you can force an attack to miss you.
Leaf on the Wind - Lvl 17 The damage from redirected attacks is no longer halved. You can now gain additional reactions as long as you have Ki to spend.
Leaf on the Wind should actually make you vulnerable to piercing damage. 
Granting extra reactions then converting those reactions to other moves seems a little clunky and risks the issues brought up by Yunru.
I'd suggest the abilities allow you to spend ki to grant the ability directly with perhaps a "You can use this ability any time where you could use a reaction." proviso if you feel the need to keep them similar.
5e is based on action economy where PC's get a maximum of 5 activities per round:
1. Partial move
2. Action or bonus action
3 Partial move
4. Bonus action or action (which ever you didn't do in #2)
5. Finish up move
The purpose of that is to keep the pace of play reasonable. I would be good with using a ki point to gain another bonus action, but you can't move after taking a bonus action.
You still end up with the maximum 5 activities:
1. Partial move
2. Action
3 Partial move
4. Bonus action 1
5. Bonus action 2
The pace of play is maintained, and the monk is doing something that no other class can do (take 2 bonus actions per round) for a reasonable price.
On further thought, I would let you spend 2 ki points for 2 bonus actions, but you can't split your move the round you do it.
As Yunru said, any 3rd lvl ability has to be scrutinized since it will likely encourage a 3 lvl dip into a class.
A 3rd lvl monk has 3 Ki, and can use 1 Ki to dash, disengage, dodge, or use FoB as a bonus action.
The simplest application is an ability like Deflect Missiles that allows you to reduce the damage of melee attacks that hit you.
Way of the Leaf:
Deflection:
Starting at 3rd level, you may use your reaction to reduce the damage of a melee attack that hits you by 1d10 + dex + monk level. If you reduce the damage of the attack to 0, you may spend 1 Ki point to make a melee attack against an adjacent target using the attacker's weapon. This weapon counts as a monk weapon and you are proficient with it. Use of this feature does not disarm the attacker.
If that's not strong enough for you, you can add this:
If hit by a shove attack, you can use 1 Ki to maintain your position and use the forward momentum of the attacker to throw them over you, sliding them into a space adjacent to you. If that space is occupied, the attacker moves into an unoccupied space adjacent to the occupied space, and both the attacker and the creature within the occupied space take 1d4 damage (+ your strength or dex mod).
It reminds me of Tai Chi.
I would try to avoid any feature that grants extra actions. The game is designed to only allow 1 bonus action and 1 reaction. Try not to break that basic design. And if you feel inclined to do so, try just an increase of +1... 2 bonus actions or 2 reactions. Jumping straight from 1 to 1 to 3 (1+ 1/2 dex) or even 6 (1+ dex bonus) is a considerable increase.
Adding a Ki requirement makes it more balanced, both overall and for dips.
Does the name come from the story about testing a sword's edge by sticking it into a river?
(For the uninitiated, the story is that the first swordsmith put his sword in the water and all the leaves that drifted against it were cut in half, without otherwise being disturbed. The second guy put his sword in the river and all the leaves went around it. Or maybe it was two samurai bragging about their swords, but same point.)
StarTwister wrote:
Elfcrusher wrote:
Actually the basis for this monk style is from air bending philosophy from Avatar. There is a great fight scene in the Last Airbender where Aang wins a fight against a student in a fire academy without throwing a single punch or using any airbending. That is the kind of fighting style I wanted to try to capture. Thanks for all the input I have a few ideas now on how to tweak it, ill put up a revised version once I have a bit more free time.
https://www.youtube.com/watch?v=1r3ADU4CoVo&feature=youtu.be&t=1m14s
StarTwister - Can the monk still attack on his turn and then use the addtiional reactions? I think the way to keep this from breaking the action economy would be that this feature can only be used if the monk did not take the attack action on her turn. You may need to add some sort of taunting ability at 6th level to goad enemies into attacking the monk if you go this route.