I have flattened boards with a random orbital sanders before, you will need a straight edge to mark all the high points with a pencil and sand them down. With a good straight edge you can get the surface extremely flat. I recently used a long steel Starrett straightedge and a orbital sander to flatten a massive table top made from sandwiched 2x4s.
A quick, but not as accurate, way to find all the high spots to sand down is to use a pencil and cover the surface with lines. Evenly, lightly sand the entire surface with the sander, all the high points will have the pencil marks sanded off. You will still need a good straight edge to check you work after, to make sure your not sanding the board concave/convex.
You can also use a cheap hand plane like one of these http://amzn.to/2ueZrIT
as a hand plane will work a bit better than the orbital sander for this. Less dust too.
But if you have a router, make a "router sled" to flatten the surface. A router sled will work better than an orbital sander and routers are a fairly common cheap tool.