Hi @mjgreg
Yes, you would be able to create a button via column formatting, this button can trigger a flow and ask for your input. After that input the flow will copy the file. Below is an example of such a concept.

1. Create a flow with three actions. Use the SharPoint For a selected file trigger. Use a text input and add drop-down list of options. Populate this list of options with your destination Dropbox folder names and configure it to use your source SharePoint document library. This dropdown list is static.

2. Add a get a SharePoint file content using path action and DropBox create file action. You can use the filename from the trigger to get the file content. You can use the file content, file name and folder name to create a new file in Dropbox.

3. Make a note of your flow id

4. Go to the source document library. Add a button column (single line of text) to the source document library. Format this column and add the json. Adjust the flow id with your flow id.

{
"$schema": "https://developer.microsoft.com/json-schemas/sp/v2/column-formatting.schema.json",
"elmType": "button",
"customRowAction": {
"action": "executeFlow",
"actionParams": "{\"id\": \"613d895a-038b-46cd-8435-efde0da2b441\"}"
},
"attributes": {
"class": "ms-fontColor-themePrimary ms-fontColor-themeDarker--hover"
},
"style": {
"border": "none",
"background-color": "transparent",
"cursor": "pointer"
},
"children": [
{
"elmType": "span",
"attributes": {
"iconName": "Copy"
},
"style": {
"padding-right": "6px"
}
},
{
"elmType": "span",
"txtContent": ""
}
]
}