Is there some kind of bonus for continuous FREE DOGE claiming?

Yes, there is. When user keeps claiming DOGE without skipping a day, his daily bonus starts growing. For example, on the second day of continous claiming the bonuses are: 1 DOGE for Basic user and 10 for Advanced one, on the 10th day they are 5 and 20 DOGE for Basic and Advanced accordingly.
In addition, there is a large bonus given each 30 days of continuous claiming. For example, on 30th day users receive: 20 and 100 DOGE, Basic and Advanced. On 60th day they get 30 and 200 DOGE. And so on. See the full progression HERE