This build might be effective in lane because of zoning with the plants, but once teamfights begin it will be worthless. The plants are easily killed when you have 5 people, especially when it comes to aoe damage.
The items that are listed severely reduce Zyra's AP which means her spells will be a lot weaker than with a traditional build, and let's be honest most of Zyra's burst comes from her ult and Q which require as much AP as possible.
I don't see this build working at all except in a 1v1 situation.
SOTEl: you should definitley drop it. The plants dmg scale with ap not ad. And the passive alone wont be that usefull.
Banner of Command: Seems kinda gimicky, why increase the dmg by 15% fi yu could just go straight ap and buff your other spells aswell. However if you play a push comb the active might get funny. It might work but a true ap item might be better.
Rylais + Lyandras: I build them every game on Zyra. The burst dmg might be lower than compared to a ROA, Rabadons build but the utility it provides is insane. And lets be hoenst if you want a hard nucker you would not pick zyra. Lyandras is really good in taking objectives like dragon or baron, and it provides awesome poke. You can put your q plants under enemy turrets to get some free harass from a safe range (that dot burns quite good). Also the sustain dmg is nice to bring down bruisers and tanks (%hp you know^^).
I think its a very good alternative since her ap scaling is not that overwhelming (not bad but just not too high either), while her flat dmg is quite good -> mpen builds are good. The only reason not to go that build is because you need an early Zhonyas or you really want that burst for your teamcomp (like if you play with a khazix, so that he gets his resets faster).
"The plants are easily killed when you have 5 people, especially when it comes to aoe damage."
As far as my experience goes , no one ever focuses plants in teamfights and if they do, well better than your carry. The only problem is that if you die, the plants die aswell so staying alive is key. So dont play it against assasins or maybe a karthus