I don't think that there is an easy way to do that.
I had a look at Custom actions that could help you in the old interface but I can't find a way to find a url to the manual triggered Flow. Also the dialog that Flow gives you is modern, so I would be surprised if you could do this.
One way that migth work is create a PowerApp and put it on traditional page then let users start the flow from there. But then the issue is that you will not have the list items/list view available. But it could potentially work with a bit of PowerApps app development
Do you want to start your flow from Flow Launch Panel of SharePoint lists or libraries?
Thanks for your feedback, starting a flow from Flow Launch Panel is not supported in Classic Experience sites currently, starting a flow from Flow Launch Panel is only available on all modern SharePoint lists and libraries currently.
If you would like this feature to be added in Microsoft Flow, please submit an idea to Flow Ideas Forum: