Do I need a vent on this emergency drain?
If it's really an "emergency" drain - one that you will never use in normal circumstances - then it shouldn't be connected to the rest of your plumbing at all.  It should just have a straight pipe leading into a basement sump pump, outside the house, or even into a crawl space (just put some screen over the open end to keep critters out).  The reason for this is that if you connect it to your normal plumbing, you will need a trap.  The trap stays partially filled with water to keep the smell of the sewer from entering your house. Over time, the water in the trap will evaporate, letting the sewer smell enter your room.  In a drain that gets regular use, this is not a problem, since you refill the trap every time you use the drain.  I'm guessing your "emergency" floor drain is only there to get rid of water if the washing machine malfunctions and overflows.  In that very rare scenario it's not a big deal to just let the water run into your crawlspace or yard, although directing it to a sump pump (and from the sump pump into your yard) is probably the best option since it keeps the open end of the pipe inside your basement if you have one.