This is not possible because the TextBlock.Inlines property is not a dependency property. Only dependency properties can be the target of a data binding.
Depending on your exact layout requirements you may be able to do this using an ItemsControl, with its ItemsPanel set to a WrapPanel and its ItemsSource set to your collection. (Some experimentation may be required here because an Inline is not a UIElement, so its default rendering will probably be done using ToString() rather than being displayed.)
Alternatively, you may need to build a new control, e.g. MultipartTextBlock, with a bindable PartsSource property and a TextBlock as its default template. When the PartsSource was set your control would attach a CollectionChanged event handler (directly or via CollectionChangedEventManager), and update the TextBlock.Inlines collection from code as the PartsSource collection changed.
In either case, caution may be required if your code is generating Inline elements directly (because an Inline can't be used in two places at the same time). You may alternatively want to consider exposing an abstract model of text, font, etc. (i.e. a view model) and creating the actual Inline objects via a DataTemplate. This may also improve testability, but obviously adds complexity and effort.