I believe this startup is as close as it gets (for now!) to what you're describing, https://www.transcriptic.com/ . (I don't work there or anything)
There's been quite a few efforts in this. See Transcriptic and Emerald Therapeutics ( http://www.emeraldcloudlab.com/ ), while there's the more traditional suppliers for things like short oligos or expression vectors ( https://www.dna20.com/ and http://www.idt.com/ ). I think there's also been a lot of independent academic attempts at this (see: http://klavinslab.org/ which is CS/BioE at UWash), but all kind of waded…
Transcriptic, on the other hand, started taking orders six months ago and has customers at Stanford, Caltech, Harvard, and more.