Oscar, that's going to depend on your RSC and DSC.
Part time is a no-go for some, and just fine for some. Work it out with them. Personally I would never go beyond part-time with them until you can generate a substantial income for yourself. Once you blow through your contacts you're going to have to do lots, and lots, and lots of cold calling. Understand that very few are able to make this a permanent career. I made the mistake of returning a phone call to them a year ago and going full time.
In addition, you have a license to sell insurance. I would explore other avenues as well with that license. Aflac isn't the only game in town and it's not a capture agency.