Let's say I have Zarathur at a planet, with a Flamer who has a Mark of Chaos attached. My opponent has a single army unit present.

As an action I sacrifice the Flamer, and use Zarathur's ability to increase the damage dealt to 3. Sacrificing the Flamer will also trigger the Mark of Chaos ability which, I assume, I could also increase using Zarathur's ability, inflicting a further 2 damage.

Assuming the above is correct, would the damage from the Flamer be dealt first, with an option of shielding that, and then the Mark of Chaos damage be dealt, with another option of shielding that damage. Or would the damage from both effects be dealt together, with a single opportunity to shield the total amount, i.e. 5 damage.

I feel from looking through the rules both sources of damage will be assigned before the option of shielding occurs.

Any thoughts or clarifications?

They would be two separate packets of damage.

Shielding can be done whenever a source of damage is dealt (not just through combat actions) so this option always remains available to a player so long as they have shields available (and a card effect does not prevent their use).

In your example that would be two sources of damage, so two shielding opportunities would be available.