Specifically, from the terminal on Clinton which is near Union Station. That’s the Blue Line right?
(I have to find when I have to leave Milwaukee on Amtrak to find out when I’ll be at Union Station to find out when I need to be on the El to make it to O’Hare to catch a 8:30 PM flight.)
The Blue Line is the line you’ll need. Give yourself an hour, although you’ll likely beat that. (That’s an hour to get to O’Hare. You’ll of course allow the usual additional time to check in once you’re actually there.)
And the 2 mile walk from the train to your gate. 
I agree. Having done this several times to get home from college, you’ll get out at Union Station. The closest stop, Clinton, is about three blocks away and is a pretty short, safe walk. It’s actually under an expressway. It can be kinda confusing to get out of Union Station and on the correct street and going the correct way. Clinton is a blue line stop, so just get on the subway going towards O’Hare, which is the end of the line. It’ll be about an hour. You’ll be underground in the Loop for a while, then on the El, then finally just at groundlevel. To get out of there, go up the escalator and hang a left (though it might depend on the airline.) There’s a bit of a walk, but eventually you will come up to terminal level at the desks. I would try to get into Chicago no later than 5:30 PM, and probably a bit earlier to allow for delays at any point of your travel. Personally, I would shoot for 5 or even 4:30. Trust me, when your connection is running close because of flight delays due to weather in St. Louis and then some jerk releases cyanide inside the Loop and you have to catch a cab just to get to the train station on time, you’ll be wishing for as much of a cushion as you can get.
You also won’t be the only person on the El doing this. Just try not to bring too much luggage, as it’s pretty full during rush hour.
Here’s a CTA map:
http://www.yourcta.com/maps/systemmaps.html#a
Here you can look at various O’Hare maps to find your terminal:
http://www.flychicago.com/ohare/terminals/terminal.shtm
I think the CTA (El train) comes into the basement of Terminal 2.
You might find the RTA’s (Regional Transit Association’s) Trip Planner useful. According to it, it’ll take 45-50 minutes to get from Clinton to O’Hare on the Blue Line, depending on how long you have to wait for a train.
Consulting the Amtrak website: The train arriving from Milwaukee around 4:30 would definitely give you ample time. The train arriving in Chicago around 7:20 would definitely not. Seems like a pretty clear-cut choice.
While usually going for international flights, I used to reckon on 45 minutes from the Loop to O’Hare and that’s probably reasonable in general. But the only time I’ve had to run from check-in to the gate was also based on that reckoning 
Though I did make the flight.
Another Chicago Doper here one who has actually done the Amtrak-airline connection. Yes, most definitely allow at least an hour from Clinton to O’Hare. It will be the height of rush hour, and in the Loop area (where Union Station and Clinton are) you’ll be wading through hordes of rush-hour commuters just to walk from point A to B.
Hope you get the ‘wacky’ drinkcart guy. You’ll know who I’m talking about if he’s on your train.