AA only flies from PDX to DFW. There's a twice-daily ORD flight, but it's seasonal (if we're lucky).
I'm pretty sure that BA doesn't codeshare the DFW-PDX flights, so I think you're SOL. On the other hand, BA partner AS (Alaska Airlines) flies from PDX to SEA (half-hourly), YVR (three daily), and SFO (five daily), so it's easy to fly to a gateway city and connect. The SEA-PDX flights are particularly cheap, quick and efficient.