First of all : This [Ash Prime] Blade storm build works with this [Innodem] build : Innodem

Foreword

[Ash Prime] 4th Ability Bladestorm does Finisher Damage to targeted enemies and uses player's melee weapon as a base melee stick so :

We need : [Rising Storm] for a combo count increase with each finisher we perform on ennemies, increasing also the combo count of [Innodem], our melee weapon
We need : Silence power from [Banshee] and [Savage Silence] augment mod will increase Finisher Damage by 564%, you can replace Teleport or Shuriken by Silence as you wish
We need : Arcane Melee Duplicate to strike twice with Blade storm without recasting it
We need : Arcane Blade Charger on primary weapon for a melee boost damage by 300%
We need : [Innodem] for it's finisher damage in Evolution form and it's pretty high base damage ; This weapon in particular for it's finisher damage, another stats stick wouldn't work as well
We need : [Finishing Touch] (+60% Finisher) and [Covert Lethality] (+100% Finisher) both for finisher damage bonus on [Innodem]

Archon shard

For the shard take whatever you want
Personally i like to go with Amber Archon Shard for casting speed and multiple Crimson Archon Shard for Melee Damage

Playstyle

So basically, you cast Silence for damage bonus, you mark enemies with Blade Storm and the ability kills every living thing you've marked. Everytime it hits, the combo increases, and if they're not dead yet, recast and mark again. Nothing should resist.
Easily clear any ennemies in Steal Path and in Netracell
And every kill you make with Blade Storm increase your melee weapon initial combo for the rest of the mission with Melee Crescendo, this means Blade Storm ability will do more and more damage throughout the mission along your melee weapon.
But I prefer to use Melee Duplicate for 6 strikes instead of 3 strikes usually.

For Operators : I prefer Zenurik for it's energy supplies, but Unairu works well too for armor reduction

Arcanes

Arcane Trickery is very useful, because if nobody can see you, nobody can kill you :)
Arcane [Fury] boost Blade Storm damage because almost every hit with the ability is a guaranted critical hit

Can replace Arcanes with : Arcane Ultimatum, Arcane Stike, Molt Augmented, Arcane Reaper