As Espio does not appear in Sonic Chronicles: The Dark Brotherhood or its comic adaption, Shade's only appearances, the two have never met. Due to Ken Penders' lawsuit against SEGA and Shade's similarities to his character Julie-Su, it is unlikely Shade will appear again, meaning Espio and Shade will most likely never meet.
The closest mutual associate of the two is likely Knuckles the Echidna. Knuckles and Shade had a close friendship in Sonic Chronicles after she joined forces with Sonic and his friends. Knuckles was originally a member of the Chaotix, and as such, could team up with him in Knuckles' Chaotix.
One similarity between the two is that both characters can be considered stealthy, as Espio is a ninja with the ability turn turn invisible and Shade is highly trained in the arts of stealth due to being a former Nocturnus Clan spy.