@ Maherees ... did you finally decide ?
I have to say that I get confused when people talk about a bike with flat bars being better for the back.
On a road bike, most people never hold the drops as they hold the hoods. My Fuji flat bar road bike keeps me at the same angle as holding the hoods. This is what I want. For this, the frame has to be longer than a bike with curly bars. Examples of flat bar road bikes are Whyte Sterling etc (they even list them under "road bikes"), Giant Fastroad, Canyon Roadlite. The ideal titanium would be a Snowdon Paradox for a mere £4k ...
Most bikes (non-MTB) with flat bars are actually 'road bike frames with flat bars' rather than 'flat bar road bikes' ... so the frame is too short resulting in having to sit fairly upright. These I call shopping bikes, including some rather expensive shopping bikes, such as Specialized Sirrus, BMC etc. If the frame is too short, sitting too upright, then on a steep hill you could do a wheelie ... which might not do your back any good at all. Of course, if you really want to sit upright, then that's fine, but it's not easy for people to identify what's what.
Some firms these days categorise flat bar road bikes as "fitness" bikes ... but not in the UK as that's something in the gym. In any case, you still need to check the geometry. You might get away with putting flat bars on a road bike frame bigger than you'd use for a curly bar bike, but the wheelbase is usually too short, your feet might hit the front wheel, you might do wheelies and you might do yourself a mischief if the standover height is excessive.
In short, there's not a lot of choice in flat bar road bikes and identifying them isn't easy.