first of all Flow doesn't strore documents. Can you explain where you would like to store your documents? Is this within a SharePoint document library?
You could use PowerApps to create an app that can receive a document and then let your flow start from there? Can you give some more details on the process around your question?
If your question is is there an action to upload a document? Then the answer is probably no. But depending on the way you start the flow the qquestion you will also have to answer is who is running my flow. If for example a flow is triggered by the creration of an item you will run as the flow owner ( where is this persons desktop?) If you manually start a flow form within SharePoint or something else you migth find that you run as the user starting the flow.
What is the form that you mentioned and would like to add a button to ?
Do you want to add a button to update documents from a desktop?
What will you do with those uploaded documents?
I have made a test on my side to save those the uploaded document in my onedrive for business as steps below:
Add trigger “Manually trigger a flow”, add a “File” type of user input, this field would be used to save the file content, add a “Text” ” type of user input, update the field name to “File Name”, this field would be used to save the file name.
Add action “Create file” of onedrive for business Connector, choose the path to save the file in the “Folder Path” field, choose the “File Name” dynamic content of the trigger in the “File Name” field, choose the “File Content” dynamic content of the trigger in the “File Content” field.
Run the flow, you could choose the file from your desktop in the “File Content” field, fill in the file name in the “File Name”, then the flow would run successfully as below: