I don't think that's an API that can be supported in Codename One.
Unfortunately I'm not familiar with Apache Thrift. From the looks of it this seems like a code generator, you can probably adapt it to generate Codename One code instead of the JavaEE/SE/ME code it currently generates.
Looking at the code it doesn't seem like it's something that's easily fixable. It is a low level binary protocol which would be a pain to adapt although doable.
You can use a server side proxy that calls thrift and communicate with that using a more "normal" API but obviously this might be a pain too.
Another approach is to use the native versions of the various OS's and wrap them in native interfaces. That would be a pain in its own right but potentially doable. I think a REST approach would be simpler.