If Washington had value as a flex getting 10-15 total touches a game, I see no reason why Greene wouldn't as well.
Greene isn't going to overtake Jones without an injury this season......but that doesn't preclude him from being a productive player for fantasy. How many years is it going to take before people realize that if a team runs it enough they CAN support two runners from a fantasy perspective? I think the Jets have an excellent chance to wind up one of those teams: They have a great OL, a coach with a proclivity to run it a lot, a rookie QB who's been backsliding, a strong D, and a home field that will have some really lousy weather in the second half of the year.
That said, I don't think Ryan wants to run Jones' 30-year-old body into the dust if they have playoff aspirations, so I don't expect him to just absorb 90% of Washington's workload. I can buy him seeing more third down work now, but that may mean they just give Greene a series or two during the game in an attempt to keep Jones as fresh as possible.
The Jets still have the Panthers, Bucs, and Bills on the slate going forward. Those contests probably bode well for BOTH Jets runners. Hell, most of their remaining opponents are exactly world beaters vs. the run(Colts, Pats, Falcons, Dolphins and Cincy). Statistically their toughest draw is probably the Bengals, and they don't play them until week 17, so for most leagues they aren't relevant to the equation.