I was under the impression that there was a dialect continuum in northern Germany/Denmark at the time. If so the language of the Angles should be near the middle of the dialect continuum of Jutes and Saxons? Then why is it that when they migrated to Britain the West Saxon dialect and the Kentish dialect are very similar and both are very different from the Anglian dialects?
Because the idea that each region of England was settled exclusively by an ethnically and hence linguistically, homogeneous tribal group with a direct antecedent to a tribal grouo/geographic area in Northern Germany, Scandinavia, and Frisia is false. It's the legacy of Medieval writers, namely the Venerable Bede, but it is inaccurate. The Anglo-Saxon kingdoms were settled by continental and Scandinavian settlers, but also by people from Ireland, Scotland, Wales, and not to mention the native British population. This process was not as neat as our sources would have us believe with all of the Jutes settling in one area, and the Saxons and Angles following suit. Archaeology has shown the diversity in cultural influences on these kingdoms, from Francia to Sweden to Ireland and everywhere in between.
As u/Steelcan909 notes, the picture of settlement is far more nuanced than that indicated by Bede. However, your question refers to the relative similarity between the Kentish and West Saxon dialects, in comparison to the Anglian dialects. Although East Kent has produced a lot of archaeological material of a Jutish character, West Kent seems to have been much more Saxon.