Have a look at the Plugin Host example in the “extras/audio plugin host” folder. It uses an AudioProcessorGraph which allows you load up and connect plugins together. To be able to load the VST’s you’ll need to make sure the project can find the VST SDK. The default for the Plugin Host is set to c:\SDKs\vstsdk2.4 on windows and ~/SDKs/vstsdk2.4 on mac.
To run the audio from the file through the graph you will need to create a plugin of your own. It doesn’t need to be a VST, it can be just an internal plugin using the AudioPluginInstance class. Your internal plugin can use an AudioTransportSource to read the file. Have a look at the Juce Demo’s file playback demo to find out about using one of these.
In general, pay attention to the processBlock method of AudioPluginInstance (actually it’s from AudioProcessor which AudioPluginInstance is a subclass of). The AudioProcessorGraph is actually an AudioProcessor itself and in it’s processBlock it calls the processBlock methods of each plugin in the graph. In your internal plugin the processBlock method will be where you call getNextAudioBlock on your AudioTransportSource. processBlock accepts an AudioSampleBuffer and the AudioTransportSource needs an AudioSourceChannelInfo. So you will have to convert between these.
It’s certainly a bit involved if you’re new to it but that’s basically what you want to do.