"kindly call" is correct and usable in written English. You can use it when you are asking someone to do something in a polite or friendly way. Example sentence: "Kindly call me if you need help with your project.".
Kindly call the family if travel instructions are needed.
Kindly call for them at once, as we have had two burglaries and cannot be responsible".
MM: My law (as you kindly call it) would make no difference to serious journalism.
Mr. Brolin burst out of a niche you could kindly call small time.
She always kindly called back with his response, which invariably was a polite "no".
D'Agata's response to these discrepancies, as Fingal kindly calls them at first, is basically: Who cares?
And Mr. Horton, who produces and directs "The Philanthropist," added: "We respectfully and kindly called it the Ed Zwick Samurai School of Directing.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union