This response is based on the information provided. We suggest you discuss with your contracting team, program manager and/or legal department as appropriate.
The keys are to follow the FAR and DFARS requirements and limitations in determining if the Trade Agreement Act (TAA) applies. We suggest the first thing to do is review the CHESS omnibus contract to see if there are any terms or conditions pertinent to the situation and of course which clauses related to the TAA are part of the contract and would they apply to your task order/delivery order.
What you intend to purchase, how much you anticipate to be spending, and with whom you are considering negotiating, e.g., small businesses all affect the clauses that come into play.
While you will need to research the FAR, DFARS, and your agency's supplement these excerpts might help get you started.
"FAR 25.401 Exceptions.
(a) This subpart does not apply to-
(1) Acquisitions set aside for small businesses;
(2) Acquisitions of arms, ammunition, or war materials, or purchases indispensable for national security or for national defense purposes;
(3) Acquisitions of end products for resale;
(4) Acquisitions from Federal Prison Industries, Inc., under subpart 8.6, and acquisitions under subpart 8.7, Acquisition from Nonprofit Agencies Employing People Who Are Blind or Severely Disabled; and
(5) Other acquisitions not using full and open competition, if authorized by subpart 6.2 or 6.3, when the limitation of competition would preclude use of the procedures of this subpart; or sole source acquisitions justified in accordance with 13.501(a).
(b) In the World Trade Organization Government Procurement Agreement (WTO GPA) and each FTA, there is a U.S. schedule that lists services that are excluded from that agreement in acquisitions by the United States. Acquisitions of the following services are excluded from coverage by the U.S. schedule of the WTO GPA or an FTA as indicated in this table:"
Table not in included in the response. Table 1 to paragraph b of FAR 25.402, General addresses dollar thresholds.
"DFARS 225.401 Exceptions.
(a)(2)(A) If a department or agency considers an individual acquisition of a product to be indispensable for national security or national defense purposes and appropriate for exclusion from the provisions of FAR subpart 25.4, it may submit a request with supporting rationale to the Director of Defense Procurement and Acquisition Policy (OUSD(AT&L)DPAP). Approval by OUSD(AT&L)DPAP is not required if—
(1) Purchase from foreign sources is restricted by statute (see Subpart 225.70);
(2) Another exception in FAR 25.401 applies to the acquisition; or
(3) Competition from foreign sources is restricted under subpart 225.71.
(B) Public interest exceptions for certain countries when acquiring products or services in support of operations in Afghanistan are in 225.7704-1."
You will want to look at the complete subpart and look for scope and policy for the part in both the FAR and DFARS as well as your service supplement.