At first glance I thought this was great, but SKR brings some mighty strong math. Even before reading this though I thought the bonus to initiative was a little much. At 20th level, with a DEX of 18 (which you're sure to have) and improved initiative you have a bonus of 18! Coupled with your other abilities this puts five daggers into the faces of your enemies before they get to do anything, and if you can squeak some sneak in there they may as well not bother rolling initiative at all. It's a great idea, and seems balanced at first glance, but it's just too abuseable.
I like this archetype as it gives a different feel to the fighter class, which usually involves large damage dealing weapons.
Quicker than the eye may give the advantage of going first but it's not the most overpowered initiative bonus I've seen in the game.
The worst one I think is the divination school ability forwarned which gives an initiative bonus equal to half the wizard's level, but also at level 20 treats every initiative roll as a natural 20. So even without any dex bonus or feat bonus you're already at a 30 initiative, and if you add 18 dex and improved initiative it will always be 38.
With the knife fighter with the same stat and feat you can only get 38 by rolling a 20, which doesn't happen often.
As for the possibility of five attacks at once with daggers the only way I could see this as being over powered is if the character spent a lot of gold to buy five high powered daggers. Which very few people would spend that much on so many daggers.
And once the daggers are thrown, unless they are all returning, you won't be able to use them for the rest of the battle.