Custom annotations aren't exposed as a first-class concept on the DataServiceContext, but you can access them by hooking into the client response processing pipeline. This code will run after every entity is finished being read:
context.Configurations.ResponsePipeline.OnEntryEnded(
entryArgs => DoSomething(entryArgs.Entry.InstanceAnnotations));
Internally, the WCF Data Services Client uses a lower-level library called ODataLib (aka Microsoft.Data.OData on NuGet). The response and request pipelines allow you to dip into that lower level to get extra information when you need it, but you still get all the conveniences of using the full-fledged WCF Data Services client library. The classes like ODataEntry, ODataFeed, etc. that you work with on the processing pipelines are all part of the ODataLib API.