Your question involves two elements, each with a separate answer.
Most felons, once they've served their sentence, get their civil rights back. Getting a passport is one of those rights. Unless a judge specifically banned you from getting a passport, I'd say you can get a passport. That's the easy part.
The other element is the "fly to Canada" part. Canada has access to US criminal history records. So if you're a felon, Canada may not let you in. Best bet- talk to a Canadian consulate about a visa. Don't just get on the plane because you may get turned around at the airport, an expensive and unpleasant event for you. Work with the Canadian consulate- apply for waiver, explain what the felony was, and how you're not the same person now as you were then, etc. There's no guarantee you'll get the visa, but the hassles will be better than being denied entry at the airport. .. Good luck!
Unless conditions of your parole, if you are, forbid this, you have the right to have a US Passport. Legal status is not a question for a passport application.
I would contact a Canadian Consulate for additional information, since you have not mentioned the actual charges.
http://canadaonline.about.com/od/travel/a/usembassy.htm