If you have it set up on ST, I should mention that you can use HubConnect to integrate any supported capabilites into Hubitat--at least for as long as ST's "classic" Groovy IDE stays around. That is, assuming you don't like workarounds/integrations with Alexa, IFTTT, or whatever other options there may be.
I'm not sure how cloud-based OAuth flow worked on ST, and I've only used local on Hubitat (and not super "flow"-y...basically manually pasting keys), so you've probably reached the limits of what I know how to help with. 
Perhaps someone else will see this thread and know how to assist. In the meantime, if it's helpful for you, I did find this other thread where OAuth with a third-party cloud was discussed, similar to what you're doing. You may find it helpful:
(I know, I know, by coincidence, it also deals with Netatmo, but the idea should be similar for either.)
