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In my opinion, the easiest way to get that awesome 340 gear is through playing operations. The max level end game gear is now 344 (340 for your implants). Being a raider, I encourage that tract. Flash points and conquest grinding can get you to 340, but at lower rarities of gear and will take a much longer time and more resource grinding.
Story mode operations reward very little materials. Averaging 15 per run from breaking down the 5 green (uncommon) gear pieces that drop from the various bosses. These green gear items will match whatever item rating you currently have on, giving you no progression.
For example, if your boots are 324, and you get boots from a boss clear, you will get 324 boots. Not much progress there.
Instead of using any of this "trash gear", break it down and get the OP-1 materials out of it. Focus on running operations that have a weekly mission associated with it. These cycle weekly and can be found in the ops raiding consoles in the combat section on the fleet as well as scattered around the zones such as Oricon.
The story mode operations in the weekly rotation will reward an additional 20 OP-1 materials, effectively doubling the amount of resources you are collecting from running it. The main reward from this weekly is the upgrade box it provides you. Using this to will upgrade one piece of gear by 2 points. Everything dropping at your current level needs to be deconstructed for materials.
Story mode operations will be your singular source of resource farming, until you get more comfortable raiding. Stick around on the "Fleet" and watch fleet chat for groups forming up and jump in when you see an advertisement. Keep in mind, you need to be a subscriber to join raids and must be at level 80.
Consider joining the "Allies" channel. Type "/cjoin allies" into the text chat box to join this channel. It is by far the most active LFM channel, at least on Star Forge. Joining or forming groups in this channel can increase your chances of getting into a group of more competent, and more serious raiders (results may vary).
Join a guild. Most guilds raid. Joining a guild, and their discord, will get you a leg up on getting together with like-minded folks. This is an MMO, and one with the top tier goodies locked behind group content. Finding a group of people to consistently join for ops can help gear you and teach you the operations to help you become a stronger raider.
Your end goal with doing ops, is to be able to get into the easier hard mode raids. You will need to be able to clear the starting "Legacy" Veteran Mode raids to gather enough materials for upgrades.
Eternity Vault (EV), Karagga's Palace (KP), Terror from Beyond (TfB), Explosive Conflict (EC) have a relatively straight forward approach and a low learning curve (EC being the hardest of the options). Some raids further up the line have easy bosses, but the final boss can be a bit tricky to a new player. Keep in mind, if you are on a DPS class, you will not be bringing much to the fight at this point. The other 3-4 dps players will be effectively carrying you while you gear and learn the fight. This strategy of playing the easy HMs is harder for new tanks and healers. A seasoned tank and/or healer will need to be there with you to pick up the weight from your lowered stats.
Augments are pretty much 100% a must for Veteran Mode raiding. While you are gearing up with the above-mentioned raids, you can defiantly augment your gear to be less of a carry, but this will cost you more augment kits in the long run, which can be a challenge. If you have the support of a guild, or friend, defiantly augment your gear and follow.
I would recommend upgrading your green story mode gear to ~330-332 I.R., then augment it and start into Veteran Mode Raiding. Eternity Vault or Karagga's Palace should be your first Veteran Mode raid. The "Mechanics" here largely do not change, so you will have the simplest time farming them. A run of either Op usually takes 30–40 minutes in a PUG. Ignore the Blue gear that is dropping at the same level you already own. We are only concerned with the gear level. I would not replace my Uncommon/Green 332 for a Prototype/Blue 332. Deconstruct the Blue and get the 8 OP-1s out of it instead.
Here is a nice trick that will work for Veteran Mode Raiding. Equip a low level relic (or ear pc, but I prefer a relic as they have fewer stats to miss). The Relic needs to be item rating 316 or lower. (So ideally save a level 75 relic from your leveling.) With this equipped, every boss you clear will drop a replacement Relic, it will be Purple/Artifact quality. Yay exciting, purple gear right? Nah, deconstruct it. It will yield 15 OP-1s instead of the 8 you would have gotten from a piece of blue gear.
This will substantially increase your yield from farming Veteran Mode Operations. 75 OP-1s from the "Low Level Relic Bait Trick" vs 40 from normal blue gear drops. If you are lucky enough for the raid you are doing to be in the mission console, it will reward an additional 65 OP-1s for mission completed, as well as an upgrade box. The upgrade boxes will give you that +2 upgrade. I recommend equipping those. It should be opened with your normal gear on, not the baited relic, or it will just drop a 324 relic and not be an upgrade.
When you get comfortable enough with raiding, Scum and Villainy has the best farming output of the raids, as it has 7 bosses (105 OP-1s). With the weekly you are earning 170 OP-1s per run and keep in mind that the weekly can be completed 3 x per week (though your character will be locked out for the week, you can do it again, should you have alts).
In summary, the benefit of Veteran Mode Raiding
OP-1 Catalyst - point-blank and simple. 15 catalysts from a story mode raid will get you nowhere. An HM raid will yield 75, and an additional 65 if that OP is in the weekly rotation (must pick up the mission) for a full potential of 140 from an HM raid.
You can "bait" purple (Artifact) drops. Simply equip a low level relic (or no relic at all) and you will get relics from every boss. You will use these relics to upgrade to get that sweet 336 gear from the vendor.
Each gear upgrade takes 60-80 OP-1 materials to upgrade, so 1 HM raid can get you a couple upgrades vs a few Story mode runs for 1 upgrade.
If your comfort level is story mode, it is going to take much longer to upgrade you via operations. It may be wiser to use flash points or conquest to level your gear, but you will not be able to unlock the vendor for 340 without at least stepping foot in a HM raid and clearing a few bosses.
Grand total of OP-1 catalysts that you will need varies, but expect to need somewhere on the scale of 2000 to get you where you need to be.