Starter items

Core items

Offensive items

Defensive items

Situational items

Thematically, Flash is all about going fast, punching everyone in the face simultaneously and avoiding everything thrown his way.
Mechanically, Megarod and Batman's Utility Belt(modded for +10 Move Speed) make you go fast, Megarod lets you punch everyone in the face simultaneously and there is no ability to dodge an enemy's basic attacks, therefore the only way to simulate Flash's ability to dodge(making the enemy attack more to hit you) is by purchasing HP and armor(making the enemy attack more to kill you).

Items
Megarod simulates Flash's ability to strike groups of enemies at once, especially with use of his W, which is great for jungle clearing with Maur Knife 1(replace with Nil Weapon if laning). Once V2.0 hits, this item will also grant HP(boosting itself) and have a higher dmg modifier. The additional MS helps with mobility and Flash's passive for extra dmg.

If the enemy team is power-heavy start off on Bat's Belt for more HP(boosting Megarod), dmg, MS(and therefore passive dmg and skill-shot avoidance) and the skill effect, where Q pokes and skill juggling can help with burst damage against your enemy while saving Will.
Against an atk-heavy team, start with Claw of Horus for the HP(boosting Megarod), atk armor, dmg and on-hit armor stealing(basic attack + W is 5 full stacks).
Defensive: If playing with a squishy team replace Claw of Horus with Metallo's Heart. You give up the dmg for more armor and cd reduc, in addition to the aura that slows enemy attack speeds, reducing their overall damage to not only yourself but your team, which is better than stripping a single enemy's armor some. Thematically this fits with Flash moving so fast that everyone else seems slow.

My 4th item depends on if the enemy team is deterring me through high HP, Armor or atk reflect/dmg.
If they have more HP than armor I grab Huntress' for its dmg and on-hit effect(basic atk + W is 5 Huntress' procs in ~1.5 seconds).
Deathstroke's is better for higher armor teams due to its armor pen and active, as you can cut into their HP and have increased dmg against them for a duration. Deathstroke's active followed by Q, basic atk and W is a huge burst of dmg(even more with Bat's Belt, Huntress' and Deathstroke's together). Furthermore, Deathstroke's cd reduc can allow more frequent Q pokes and ult usage.
Defensive: If playing against a squishy team, trading Deathstroke's with Lobo's will give additional HP(boosting Megarod) and provide slows on hits, trading your increased skill dmg from DS' active with increased kill secure for your team.
Situational: If looking for more frequent move spam replace Deathstroke's with Blue Scarab. You retain dmg and cd reduc but replace the increased skill dmg active with increased Will Regen. On the other hand, getting Bat's Belt, Deathstroke's and Scarab provides 30% cd reduc, not counting Augments.
If dealing with atk reflect or high dmg grab Atlantis Gambit. Post-2.0 it will have HP(boosting Megarod), while also giving dmg and atk life-steal. Further, the active slows an enemy for easier kills and allows healing off of basic attacks(basic attack + W heals for 15% max hp in ~1.5-seconds, not counting the atk life-steal from the aura).


Stolen Powers
Atomic Green Lantern's Consume boosts not only your sustain but your speed(and therefore dmg), allowing for easier escapes, chases and map traversal.
Zatanna's Psychic Assault(much like Atlantis Gambit's active) is great for either distancing yourself from a dangerous foe or securing a kill. These combined with Flash's E allows for a decent amount of CC.


Augments
The bonus move speed increases Flash's mobility and dmg due to his passive. The cd reduc helps out bit-by-bit as you level(especially for your ult) with the small bit of atk pen helping make giving up either Claw of Horus or Deathstroke's for defensive options a slightly easier decision, though the pen could easily be traded for some extra atk life-steal.


Skills
The increased dmg vs increased Will cost of Flash's W makes me feel leveling it last is the most Will-efficient choice, allowing more frequent use that relies on your On-Hit effects for damage(as the skill is intended to be used), rather than your basic attack dmg. Focusing on his Passive, Q and E allows for jumps in mobility and damage(boosts from Bat's Belt) without significantly increasing Will-usage. Lacking the ranged poke of other Assassins, Flash must prioritize coming in from an enemy's rear or flanks, so that use of your Q puts you further aside/closer to your teammates, rather than nearer the enemy team/turret. The increased HP/Armor helps Flash survive the wind-up for his ult, while the MS from Megarod, Bat's Belt and your augments makes approaching enemies easier so that shorter Q dashes(equaling shorter cool-downs) can be used.

Summary
You have plenty of speed and mobility in addition to being able to tear through practically any enemy with punches that come fast and/or Infinite Mass-like while hitting everyone nearby, your HP/Armor and recovery giving that feeling of avoiding your enemy's punches/claws/arrows/bullets as they throw as many as they can to take you out.