Also thinking some goats.... possibly in the same area?
Thinking they could keep the weeds down that grow up in the straw, so that I could still use the straw around my flower beds.

Is this possible?
Any problems with the idea?

Are the pine trees growing in sandy soil? If so & it's dry the area should work for both goats & chickens. If it's a dark, rich soil it may be too wet/moist. What are you planning on using for shelter?

If the area is large enough the grass area would be beneficial. If not, the grass will die from all the scratching & trampling. Maybe it would fare better if you layed down some wire to protect the grass, yet they could still enjoy it. Dunno if that would work as I never tried it.

Goats & chickens can live peacably, no health issues between the species, unless the area became too wet.

I agree with gakaren - visit the Back Yard Chickens forum where you will get a lot of great information and ideas. I mean alot of good information!