I'm leaving for basic and AIT in one week to FLW, 74D. How does someone get onto a chem unit? Is it based on performance at AIT or random?

PFC (Join to see) Your assignment will be done based on major commands requesting from DA your MOS and Rank, DA will decide who has the greatest need and thats the major subordinate command (MSC) you will go to.
Sort of some special needs, you will have no influence in your assignment.
After you get to the post your assigned, the replacement detachment will get your final assignment form the MSC G1, so if you were to go to say Fort Hood...and the replacement detachment.. III CORPS G1 will look at requisitions for your MOS and rank and decide which division, separate brigade you would go to. If its 1st CAV, their G1 will decide which Brigade you will go to, then that Brigade S1 will decide which company you will go to.
In theory you should go to a unit with an authorized slot for your MOS and Rank.... But it is also possible to be assigned to a positon that is MOS immaterial, or be assigned out of MOS.

If say you get to 1st Cav, and they do not have an immediate need for a 74D 20 Soldier, you might stay at the Div, assigned to HHBN the Div HQ unit, and work in the G3, or the Chem section, or be assigned to the Admin section and set up chairs, conference rooms, overhead cover, tents, and vacuum the entrance way carpet for 8 months to a year before being reassigned to a unit

Per reg, there is to be a CBRN person in every unit army wide. Commonly this is assigned as an additional duty as there is a large shortage.

This makes lateral movement a lot easier if you can find a unit with a vacancy and get in contact with your branch manager.

Assignments are usually processed near the end of AIT however where you will be stationed is dependent on your service component.

In the national guard you will typically be attached to a line unit such as an air traffic control company or Transportation company but this varies and can cover anything from infantry to your battalion HHC (WITHIN THAT STATE)

in the reserves there are a large number of CBRN companies and battalions hat rotate on a support basis to where they are needed. These brigades have recently shifted to the Stryker CBRN Recon set. This requires additional training such as L6 and L5 to be qualified.
Those schools are offered at the AIT but the personnel for them are hand picked by the instructors based on scores and over all performance. There is also a consideration for the component you're in. Meaning if you're national guard don't hold your breath. If you're active you will likely be selected (so long as your are high speed) and if you are reserves I would recommend volunteering and talking to instructors around half way through although you are not guaranteed.

Note that if you do not receive this training you will likely be assigned to a line unit.

Active duty personnel are almost guaranteed not to be assigned to a CBRN unit as there is a high demand for CBRN soldiers army wide. You may very well be in a line unit as well.

On the positive side about a year after getting to your unit following AIT, there is a good chance that if you can find an empty alot in a unit then you may be able to transfer. This requires the correct paperwork and involves getting the two commands communicating. Don't be the private or PFC randomly calling CO or 1SGs asking for a slot. Go through your s1 (active) or your readiness NCO (Guard and reserve). They will point you in the right direction.

I don't understand- as a 74D you would normally be assigned to a chem unit to get trained up in your MOS, normally NCO's are the ones assigned outside the chem units to line units.