I've built doors similar to the pair you show above. Yours sure look flat... but pretty is as pretty does. Mine are flat enough to function, but it wasn't easy getting them that way. It's an art- one I haven't mastered yet. There is an original single man door. It makes yours look like they belong in the Sistine Chappel!
The two in the picture were built flat, after a few weeks they warped (not unexpected). They aren't actually doors so it didn't matter. Overall construction lumber is a bad choice for door parts for 3 reasons:
1. It's usually full of defects
2. it's usually case hardened from the kiln drying process and full of internal stress because of that. Construction lumber is dried faster than non Construction lumber because it doesn't matter to a wall.
3. It's always way to wet to build things with (typically 20% mc)
Building a flat door isn't that hard, keeping it flat is a bit of luck and lot of choices. If you start with good stile material (flat, quarter sawn or clear vertical grain and perfectly defect free you stand a good chance. If it warps while milling its not suitable, so it can be reused as rails.
The alternative is stave core construction, you can use junk in the cores as is common on 99% of commercially produced "solid wood" doors. More labor, but there is a high chance the stay flat.