Since you are redoing the floor, install a new flange on TOP of the finished floor, like it is supposed to be done. To make things easier, notch the tile on the wetsaw or with a grinder prior to laying them down so you don't have to try to drill through them to mount the flange through the tile into the subflooring. When finished, the flange should be firmly attached to the floor and not have a gap underneath it. this is much easier if you have access to the pipe from below to allow you to cut off the old one and a little pipe, then patch in a coupling, straight piece and a new flange. You can do it with an internal cutter from above, if required. Depending on the flange, you might not need a coupler and a short piece of straight pipe if it has a long enough neck.