Will my roof framing support an array of flat solar panels?
2x8’s spanning 14’ can support between 31 psf and 53 psf depending on the species and grade of your 2x8’s. 

Your existing flat roof “dead load” (load that does not change) is: 

1) roofing between 3 psf and 8 psf depending on the type, number of re-roofs, etc., 

2) roof sheathing is between 1.5 and 2.5 psf, 

3) roof joists of 2x8’s is 1.5 psf, 

4) attic insulation (if any) is between 2 and 3 psf, 

5) ceiling (if any) is between 3 and 4 psf, 

6) miscellaneous, including lights, etc. is between 2 and 3 psf 

Therefore, the total dead load is between 11.5 and 20.5 psf depending on all the materials on your roof. (Feel free to adjust my estimates depending on your exact materials.)

Generally, we add a “Live Load” (snow load, etc.) to the dead load to get a Total Load. However, you’ve indicated that there is no snow load. 

Your 2x8’s spanning 14’ At 24” on center will easily support your solar collectors weighing about 2.5 psf. 

So, the 2x8’s will hold them up, but we also worry about holding them down. If you live in a high wind area or seismic area, you’ll need to anchor the collectors to the roof too. Then, we worry about holding the 2x8’s to the bearing walls, then the bearing walls to the footings, etc. 

Btw, solar collectors are the perfect shape to fly away...be careful.