I never use that expression. Maybe I could imagine an undulatti squaking it.
"Pretty please" is used in the sense of begging /pleading, only in informal situations. Normally you'd have said please first, then this, maybe then followed by "Pretty please with a cherry on top!" Maybe it's only British English, unless I heard it when young from an American show.
"Ole" is the imperative form of "olla" (to be), so "ole kiltti" literally translates to "be kind". It is used as "please" sometimes.
"ole kiltti ja avaa ikkuna" - open the window, please
It is, however, not as neutral as "please", at least in my opinion. I would never say it when ordering something at a cafe ("yksi pulla, kiitos"), for example. Depending on the context and the tone of your voice, it can be interpreted differently. Translating it as "pretty please" makes me think of someone begging for something (like a child for a toy) etc.
The word "ole" was introduced earlier in the expression "ole hyvä" ("be good"), which again can be translated as "you're welcome", "here you are", "please".
"ole hyvä ja laita roskat roskakoriin" - please put the trash in the bin