That type of flange generally has two ways to hold the bolts...you can see the slots at the front and back. If it was rotated 90-degrees, you'd have used the bolts slid into those slots. The other way is with a concentric T-shaped slot, which is likely what you have the bolts in now. To get the bolts out, you'd need to clean up the T-slot and slide it to the wide end at the T, then pull it out.
If the flange is intact, you can get those bolts out that way. If not, then, it may be easiest to cut them off flush with a hacksaw or grind them with a grinder, then, install a repair ring, and use the slots in the repair ring to hold the new bolts. Pros tend to use two sets of nuts and washers...one to lock the bolt to the flange, and the second set to hold the toilet down. By anchoring the bolt to the flange, when it comes time to remove it, it won't spin. Also, chose brass or stainless steel bolts and nuts, and you won't have that problem. If you go with a repair ring, you'll need to clean things off more, seal the repair ring to the existing one and drill holes to screw it down. Again, use brass or SS, so it won't rust away. If you search on repair ring, you'll see some pictures of what I'm talking about.