The phrase "speak smoothly" is correct and may be used in written English.
You may use it to describe how someone speaks in a particular situation, as in the sentence "He spoke smoothly and confidently during his speech."
Mr. Zhou, who has heavy, crescent-shaped eyebrows and speaks smoothly, seemed to handle awkward situations with wit, laughing.
She spoke smoothly, often throwing in obscure Chinese idioms, which, upon seeing my blank expression, she would jot down and explain.
Someone lofty may have spoken smoothly into the ear of his lieutenant, Michael Gove, to persuade him he was prime minister material and that he should desert.
But there he was last week, at Eleven Madison Park, leading a tasting of his wines, speaking smoothly in French, gesturing with long arms that seemed as if they would be a lot more comfortable sprung from the confines of his rumpled blazer.
To hear Latin poetry spoken smoothly and quickly is to hear a mellifluous, rat-a-tat-tat language, the rich, distilled, romantic, pure, heady blueprint of its close descendant, Italian.
Were you speaking smoothly or stammering?
In fact, slowing down or pausing when you reach a stuttering obstacle can train you to speak more smoothly and with less anxiety.
Speak freely and smoothly, and speak as if to a friend to whom you have spoken for a long time.
Mr. Colla speaks the speech smoothly, sometimes while smoking a cigarette.
Alwan, a compact man with scrunchedtogether features who has been at B.B.N. for two years, spoke rapidly but smoothly, with a droll delivery.
He is agreeable company -- smoothly spoken, self-assured, courtly and low-key even when what he says or does is anything but.
