It's a colloquial AmEng expression, but it is not correct English (Am or Br) as it features an adjective 'slow' in place of an adverb 'slowly'. It doesn't make sense to use it in this context: 'playing it slow' describes deliberate restraint, usually applied to present actions: it is about deferred gratification, as contrasted with impulsive or immediate action. It might make sense to play it slow in order to achieve a sustained relationship, but this is not a good way to describe the desired end state. The end state is long term business relationship which benefits both parties: why not describe it as such?

"Play it nice and slow". Its like you want to make it safe and clear on your cooperation. seems alright, unless they would think that it feels weird (in my opinion) like you're going to give him/her something ( ͡° ͜ʖ ͡°) *wink wink* Try if you want (or not): "...and hopefully we can both satisfy our needs in the future"