I'm not aware of any reasonably straightforward way to pass form data into an HTML5 LibGDX application on the client side (ie. directly in the browser via HTML and JavaScript only). I would expect any effort to do that would get overcomplicated very quickly since the Java code is compiled down to essentially unreadable JavaScript during the HTML5 build process. There may be something clever that could be done with source maps, but its probably not worth the effort.
This may or may not fit your use case, but if you write a server-side application to handle the form data (in any server-side tech, php, node, java, etc... perhaps storing the form data in a database) then you can communicate with the server-side application from the LibGDX app using the built in networking API of LibGDX such as standard http requests.
A better alternative is probably to just create your HTML forms directly in LibGDX using scene2D UI API and then there's no separation between the input and the game. The downside to this is that if you need to change the forms then you'll have to rebuild and redeploy the game, but if your form data changed significantly enough then you'd probably have to do that anyway in order to process the new data in the game.