I have a web map application which displays WMS layers from GeoServer. I am looking to add a functionality which will allow users to click on multiple map objects. The application will then generate a bar chart based on the data of the selected objects and presented it to the user. Any hints or guidance on how to achieve this would be greatly appreciated.
I'm not sure about what you mean the "map objects" and how you serve the "data of objects" in the question. Are they vector features on a vector layer that you added to map, or just the objects come with the wms layer.
If they are vector features, you can easily get the feature information (data) via OpenLayers API. If the objects are inside the wms layer, then probably you can have a look at this example, get feature's information via Openlayers
WMSGetFeatureInfo control. Please note there are some prerequisites for this control to work.
After you get the data, store them and organize them in a readable way by the chart library you use.