Forewarning: While I am going to be starting this I cannot recommend it, this isn't a build guide, more an exploration on how Alchemist's Mark could be built. If it ends up being excruciating I am going to pivot to either Bane, or dslily's poison BF/BB. Please let me know if this sparks any ideas, or if you see anything glaring I missed.

Like a lot of people I get excited about new skills and feel the need to run them even if it's not going to be an ideal situation. Alchemist's mark caught my eye as something cool to build around, being able to snap shot DoT damage and have it affect an AoE is something exciting in my opinion.

I went with Occultist for scaling curse effect, plus the profane bloom and innate wither stacks will help the build limp along. I originally tried PoBing out a Pathfinder/Deadeye for poison prolif and mark effect, but didn't like the look of scourge arrow numbers.

Key Pieces of the Build:
Cane of Unraveling is pretty self explanatory for any DoT build, eventually you will want a +5 staff with chaos DoT multi but that is quite a bit of investment on top of what we have here.
Crown of the Inward Eye: We travel a lot and are pretty thirsty for mana, it would be hard giving this up.
Blackflame: We are going all in on the meme and trying to have burning ground and poison ground. This allows our ignite damage to scale by reducing chaos damage, as well as helping with wither uptime. With this and flammability we end up with 50% ignite chance on bosses and 80% against normal enemies.
Vixen's Entrapment: This is what automates our supplemental curses and Alchemist's Mark. Each time we cast our Despair w/ Impending Doom we will also trigger Temporal Chains, Flammability (or if you would rather Enfeeble or Punishment), and Alchemist's Mark. The chest in the PoB has a +1 curse that I am currently not taking advantage of because when fighting a pinnacle boss you could swap these out for gloves with better stats and the eldritch implicit with mark effectiveness when in the presence of a pinnacle boss (30% max I believe?). Additionally I think that arcane surge can be linked to triggered skills which automates that as well for us.

Overly optimistic/PoB warrior DPS against pinnacle bosses came out to 4,373,136. This assumes you instead use a double 5 link of blight/ED alongside hexblast and the boss is kind enough to stand in both pools while you channel blight.

Problems I already see:
We are stretched pretty thin everywhere getting what we want to have a working build. Which will make solving problems down the line difficult.
Mana, as with above we don't have great ways (that I see) of adding mana to the build. After we cast our curses we're going to be running on fumes, thus the enduring flask and arcane surge.
Ailments. Maybe some change up of flasks with pantheon can make this better, but for right now we are relying on softcore and controlling enemies.
Ignite chance. We can get the jewels for Shaper of flames and solve this, but that is a significant chunk of change. I am operating under the assumption that since the ignite lasts for a while and we can only create a pool occasionally the 50% against bosses will be fine, but in reality I can see having a dry streak, then getting a pool, then the boss teleports.
Napkin math: I put my math in the notes section, there's certainly the possibility of mistakes. Also I suspect the burning ground will deal less damage than I have listed. While our ignite will deal chaos and thus have its damage boosted by reducing that resist, the burning ground will still be doing fire damage and thus only flammability impacts that.
And the most obvious: Cost to performance. Every divine we put into this would be better off in a more consistent build.

Pobbin: https://pobb.in/sM-8BYzSxLs-