No, usually you cannot do this. The reason for this is a flush mount fan has a plate that mounts both to the box, and to the down rod. This plate also has a hanger. You can try looking for a shorter down rod though. The places you can find the shorter down rod are Lowes and HD. You should be able to find a short down rod all the way down to 4 inches.
You can also look at our hugger & flushmount ceiling fan pages, in order to find a replacement fan as well. You may not like your normal ceiling fan as much and just thinking of replacing it with a hugger or flushmount replacement. No problem. Browse on the left hand side to the Hugger Ceiling Fan page and try taking a look at that, in order to find a fan that you’re interested in. We do our best to find the right models for you as well. Please let us know on the contact us page if there is a certain fan that you’re after and unable to find here. We also respond to part requests as well.