I ok I misunderstood, I thought you were implying that you would move into the duplex and rent out your old house after your parents move out. And by cashflow I meant would it cashflow when rented. But I understand your situation.
Some tips to consider
2 bedroom units - I can find a duplex with 2 bedroom units and one with one bedroom for the same price 2 bedroom makes more money and seems to attract more long term tenants.
Split utilities -or the possibilities to split not a lot of people talk about this one, but a change in purchase price of 20k or even 50k (when buying with a 30 year mortgage) makes very little difference in the payment. Common utilities could cost 200-300/month, if your goal is to hold a long time and cashflow, split utilities make a huge difference, I think for some reason most renters don't look at this in their process.
Watch the neighbors - an attached building can cause you major headaches....if the building next door gets cockroaches they will come over into your building and you may have to let tenants out of leases, because spraying your building won't get rid of them, and getting access to the other building may not be easy....I guess I don't have to tell you where this example came from. So what do you watch for....neighbors that are owner occupied and long term as well as maintaining the outside of their building...but the biggest thing would be what I'll call peer pressure from the neihborhood, if most people on the block are keeping their place nice it is more likely that it will stay that way. This seems to hold true even to the lowest income level neighborhood. A good mix of owner occupants I a block or said another way their is maintained landscaping in front of houses, is a good indicator.
Separate entrances - not having common areas with common electric bills snow removal requirements and yard mowing makes a big cashflow difference, and again I have found that this doesn't change the houses purchase price.
Harder to sell - less buyers for multi family, so if you change your mind a lot you might want to think before you act.
Mls is a good start, ask your agent to setup a report which sends you an automatic email every time something in your criteria comes on the market....I watch all multi family in my area and get a daily email on it. I have also bought on Craigslist.
And a final tip for buying. Be friendly with the sellers, in multi family their is a good chance that the seller has multiple properties, and also a good chance that they are selling them, if you find a good property that has all the things you like and is well maintained...good chance that sellers other properties will be good. If you are buying distressed just look for good bones.