Add the JS script as an external script and insert the IN/Share
element anywhere in the app where you would like the share button to appear. Here is an MWE,
import dash
import dash_html_components as html
app = dash.Dash(external_scripts=["https://platform.linkedin.com/in.js"])
app.layout = html.Div([html.Script(**{"data-url": "https://platform.linkedin.com/in.js"}, type="IN/Share")])
if __name__ == '__main__':
app.run_server()