No, there is no such capability in the Shuttle / ISS era US EVA suits (Extravehicular Mobility Units - EMUs).
The suit contains a separate Secondary Oxygen Pack that is only used in the case of emergency. It provides approximately 30 minutes of O2 - enough to return to the vehicle. But there is no cross connection capability to another suit.
Source (old, and for kids, but still the best description on the internet I know of)
Edit: It's hard to prove a negative, but I can also offer up the EVA Checklist. If you look at the Cuff Checklist (which is the checklist attached to the crewmember's wrist and which contains emergency response procedures) there is no reference to any buddy-breathing system. Here's the table of contents.
SUIT P EMERG just sends you to ABORT EVA which sends you back inside. So does SOP O2 ON which indicates the Secondary Oxygen Pack has been activated.