… seems I can’t edit my replies to add add’l thoughts or fix typos …
So, by the previous comment I mean… I can use this JSONPath expression string to get to [extract] a button’s text color from the large JSON object returned using the /nodes API call:
$..document..children[?(@.type==='TEXT')].fills
Be aware, this is for OUR design file. Yours will almost 100% need a different path to get to the figma spec definition you are interested in.
But that aside, the benefit of JSONPath expression strings is the ‘shortcut’ of ‘…’ that can be used to skip all the in-between levels. Since, as our design team structured their design file, this particular button’s text definition, searchable using the filter expression above, is technically at the following fully qualified path (which JSONPath-Plus will also give you):
"$['nodes']['3:1515']['document']['children'][0]['children'][1]['fills']"
And finally, the JSON object value that is extracted from the JSON object the API for the node_id of the button in question that contains the button text’s color of ‘white’ is returned as:
[
[
{
"blendMode": "NORMAL",
"type": "SOLID",
"color": {
"r": 1,
"g": 1,
"b": 1,
"a": 1
}
}
]
]
…Ya, a single API call that returns #FFFFFF certainly would be better. lol. But this way, we have a job, right? 
(I was given rights to edit my posts. So I updated and fixed the formatting of my text above.)