A starting point might a SQL query like
INSERT INTO kimai_knd ('knd_name') SELECT customer_name FROM old_table
This copies all values in the column
customer_name form table
old_table into the table
kimai_knd in the column
knd_name.
Information about the INSERT INTO ... SELECT statement can be found for example at
http://www.1keydata.com/sql/sqlinsert.html . If you need more information about this use your preferred search engine.
Also don't forget to add an entry into kimai_grp_knd for each new customer. A spontaneous idea:
INSERT INTO kimai_grp_knd ('grp_ID', 'knd_ID') SELECT 1, knd_ID FROM kimai_knd
You can execute those queries from a command line client or using something like phpMyAdmin.
I hope this helps you to find out how to do it. And please don't use your production database for testing this.

Best Regards,
Severin Leonhardt