How should I install tile backer board with a curved tub flange?
You can put backer board on top of this flange and then set the tile to overlap the flange and sit down snugly on the tub, sometimes having to bevel the back side of the bottom edge of these bottom tile with a diamond blade on a 4.5” angle grinder. But, make sure that the combined thickness of the backer board and tile will get you out far enough to achieve this. You may need to furr the wall out a bit anyways to make overlapping that flange possible. 

Before setting the tile you want to tape all joints with alkaline resistant mesh tape and use a suitable surface prep cement to fill all voids at all seams and screw heads, including the void at the bottom where the backer board sits on the flange and not down on the tub. Flatten as much as possible while the mud is wet, and when it’s set give it a rubbing with a flat grinding stone to knock down any minor imperfections. You
May need to repeat the process to get where you need to be. Apply your waterproofing membrane, then set your tile. 

Remember that tile is a surface finish, just like paint, and the quality of the prep beneath will show through in the tile. The flatter you make your substrate the easier it will be to keep the tile flat, and the easier it will be to eliminate voids and irregular bonding between the tiles and the backer, which will prolong the life of the job. 

On that note - how well in plane are the studs of the walls you plan to tile? You may need to furr studs out to bring them all into a flat plane - this is the first thing you can do to ensure success. The extra time spent here will come back to you at every other step of the process. If the walls are really bad you can run 1x3’s perpendicular to the studs, use shims to bring the 1x3’s into plane, and hang your backer board on the 1x3’s.

Maybe more info than you’ve asked for but is hopefully relevant.