I've never heard "shade" used in this way, and more context would be helpful, but my guess is that it means the same thing as "shadow," that is, to follow discretely. I'm basing my guess on the nature of the movie, science fiction, set some time in the future. In a science fiction movie there is usually some attempt to speak in a way that is conjectured as the how people will speak in the future (note the rather unusual vocabulary, "hot chicken" and "a watcher").
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