References to calculate lumber size and span for flat roof?
To calculate the maximum span of roof joists you first add up the Dead Load (weight of joists, roofing material, etc.) to Live Load (weight of snow) to determine the Total Load.
Your Dead Load is

roofing, which is going to be from 1 lbs. per square foot (psf) up to 3 psf, depending on the type of roofing.
roof sheathing is going to be from 1 1/2 psf up to 2 psf depending on the thickness, which depends on the spacing between the joists.
joists are from 2 psf for 2x6’s 12” on center, or 1 psf for 2x6’s 24” on center up to 3 psf for 2x8’s at 12” on center.
ceiling material, if any.

I’d guess your Total Load is about 7 psf, because you have no Live Load. Then you can use a joist calculator like this one:
https://www.awc.org/codes-standards/calculators-software/spancalc
You’ll notice that the span calculator only goes down to 10 psf Live Load. This is okay for your situation because you may hang lights, hanging flower pots, etc.
So, your total load will be about 17 psf. Then try various sizes and spans until you get one you like.
If you use 16” on center, don’t forget to convert your load from psf to 16” on center by multiplying 1.33 to your psf load. (So, 17 plf becomes about 23 lbs. per linear foot on your 2x6 joist. )