Starting oboe won't kill your embouchure, it will just put it into a coma.
What will probably happen is that you'll practice the oboe more than your flute and you'll really not get that good on oboe so soon, but your flute playing will plummet with neglect. So you won't play anything really well for a while.
Oboe playing doesn't really numb the lips, the vibrating of the reed is really inside the mouth. If playing oboe for a long period of time you can tire your lips and start to bite which puts an indentation that doesn't wear away too soon so it can get in the way of flute playing or you can play around it (or it could possibly go numb with severe biting, don't bite).
You may get to a point that to have high quality oboe playing or high quality flute playing you have to make sacrifices or practice a hell of a lot. The sad part is that the flute has to be that sacrifice. You can neglect the flute and have some tone/intonation issues, but if you neglect the oboe you will experience PAIN/suffocation/tone/intonation issues.
There aren't many flutists that double on oboe, they become oboists that double on flute.
Interestingly there is a saying that oboists make poor flute players. Though I think that it's people who fail at flute that find hope in the oboe.
If you really want to play oboe go rent one and find a good source of reeds (check out reedreviews.net). I would recommend finding a private teacher to help you pick out a working rental an get you started correctly. If you can play the oboe well your teacher will love it. They probably have bad oboe experiences... it can really sound HORRID when you don't practice. It's better to not have an oboist, than to have one that doesn't practice! Really!
The oboe can be fun or it can be hell. Depends on which way the wind blows. <g>