Here is a first cut at support for adding new field types to managed schema. Two things of interest here:
1) There's a whole bunch of proven code for creating a fieldType using the FieldTypePluginLoader so I chose to use that for this solution. However, it requires the fieldType to be defined in XML, hence this patch uses an "adapter" to transform the JSON from the REST API request to XML, see: FieldTypeXmlAdapter (only around 100 lines of shim code)
2) The endpoint doesn't support adding multiple field types in a single request as is allowed for fields. Personally, I think client apps should have to add one field type at a time, but if we want to allow multiple that shouldn't be too bad to add.