No informed advice to offer, as I'm sort of on the other side of your exact situation right now: my wife will be meeting my most-significant outside partner next week, if plans come off. So I'm sort of able to channel what she's said she hopes for out of that meeting to you:
She definitely doesn't want to feel she's "competing" with him right there over dinner, so any overtly flirty stuff from him would spark her the wrong way.
She does want to get to know him, a bit, without me being an overly-active mediator, so I've promised to try to let their conversation take its natural course without attempting to be a go-between. I think for you that translates to: try to talk to her as directly as possible, not talk to her through him.
She'll appreciate any PDA between me and him being kept to a publically-appropriate minimum, e.g. a strong hug at greeting and parting.
She did say to me with a smile, "You're sitting on the same side of the table as I am, and he'll be across from us." :-)
Good luck--I think just being yourself and signaling to her that you're not a threat to their relationship are the key objectives. Have fun!