Verified answer

Both conductors have to be rated for the full capacity of the load. In this case, the load sees only a single phase...what the absolute phase of each leg is at is not important, only the phase difference between the two legs. Current flows in one phase and out the other and vice versa the whole time.

Both conductors must be rated for the total current draw of the load.

What you have described is the use an electric water heater in a building that is being served with 120/208 V 3-phase, 4-wire service. This is not uncommon in condos and apartment buildings. Each tenant receives single phase service with two legs of the service and the neutral. The 120 V load is connected between one of the legs and the neutral. Larger devices such as electric ranges, AC units, water heaters, etc are generally fed with 240 V, but in this case are connected phase-to-phase and have 208 V across the appliance.

Some tenants are fed with A-B, others B-C or C-A to balance the load on the utility's transformer.

2500 watts / 208 V = 12 amps.

Each of the conductors must be rated for 12 amps. Common 14 AWG is a suitable conductor for this application.

Connecting 2500w of resistive load at 208V single phase would produce a 12A current. Both conductors would carry 12A, it is not 6A per conductor.

One reason is to reduce the current flowing in the neutral return conductor. The amount of current flowing in the neutral creates a voltage drop which results in power loss. In a balanced 3 phase system the currents flow between the phases. If it is unbalanced, the out of balance current has to return to the source via the neutral, which is the star (wye) point of the supply transformer, which is also normally earthed (grounded).

The conductor must be rated for FLA.

Yes. Look up a "grounded delta" system. Climatrol™ was very big into making grounded delta systems (also called corner grounded)