Unfortunately, there is no automated migration path from Koken to Juicebox.
You would need to recreate your galleries from scratch using JuiceboxBuilder-Pro and then embed the galleries into your web pages (assuming you have FTP access to the web space that your host provides) following the embedding instructions here.
I really dont see any shortcuts that you could take unless you are able to write a script (perhaps using a server-side scripting language such as PHP) to fetch the current image data from your database and use this information to build a Juicebox gallery's 'config.xml' configuration file. This would be a lot of work (and is beyond the scope of support that I am able to provide) and might only be beneficial if you have hundreds of galleries to convert (due to the complex and time-consuming nature of such a project).
I realise that this may not be the answer that you are looking for but creating galleries in JuiceboxBuilder (once you've got it up and running) is a quick and easy process and if you have data embedded within your source images, then JuiceboxBuilder can extract the IPTC Document Title (as the image title) and the IPTC Description (as the image caption) which would avoid the need to manually enter image titles and captions.