I would question any program that sets any of this in stone. In the big picture, the order here is a tiny detail. Which exercise you do first will have no effect on your goal of burning fat and gaining strength.
Now, here's the kicker: If you want to reap all the benefits, go for variation. Don't stick to always doing exercise A before exercise B. You should vary this.
do every other work out A->B and B->A
do 3 month cycles where you rotate which you do first
do any number of variations in between
The real goal should be to get the variation, so your progress doesn't plateau because of lack of new challenges.
To answer your questions
Why is dumbbell incline between both barbell presses?
You're getting caught up in details. I doubt even the creator of the program can tell you why the dumbbell press is between two barbell presses. Sure, you should do all of them, but you should also do a large number of other pressing exercises and variations and orders. So the order s/he presents is good.
Why do I typically not see dumbbell flat bench press in workouts (or is it just me)?
You'll find them. But in the grand scheme of things, every exercise is a detail. It's the ensemble of a hundred different exercises that give you the progress you need. Sure, any one program might not utilize a hundred exercises, which is why programs should be cycled in and out.
Is there a better arrangement than the above and why?
The arrangement is fine. Using it forever is not fine.
I am training for strength
Which order you do these exercises in has little bearing on this. Just switch it around whenever you feel like you've plateau'd.
and fat loss
Press exercise orders has nothing to do with fat loss. In fact, weight training does very little in terms of burning fat in the first place. Fat loss is primarily done in the kitchen. But weight training will affect how your body adapts to the changes, so there's that.
I lift as heavy as I can with continuous progressive overload.
This is the important part. This is the correct approach. Just remember that progressive overloading isn't just about increasing the weight, but increasing the amount of reps, and increasing the surprise-factor. I.e. exposing your body to exercise it hasn't experienced before, or that it hasn't experienced in a long time.
I feel this needs to be said. There is no exercise or program that is so good that you should do it, and only it, forever. I'll harp on it one more time; variation is key, lest your body just adapts to the routine and finds no need to get stronger.