That does look like a horizontal stem, so flipping it might not offer much. Even if it is, though, buying a different stem shouldn't be more than £20-ish and will take a few minutes to do, whereas buying new bars (and levers etc) will be a lot more expensive and take some time to accomplish.
Aside from cost issues, flat bars might be a step backwards for you, as they give positions which are no more upright than you get already if you ride on the tops and, IMO, are a lot less comfortable than drops. Flat bars have one hand position, with bar ends you might get two. Drops have at least 5 different hand positions (drops, tops, hoods, bends and holding the top of the brake levers) though, giving more flexibility to adjust your body positon to your requirements which change with the ride.
Also, your bike has no bar tape. A good, confortable tape will improve matters too, IMO.
I'd get down to your LBS and see what they have to offer for stems. Look for something shortish (to reduce the reach) and angled (to reduce the drop), they might even let you try before you buy. And get those bars taped up.
**I spent so long writing this that ck got in there with a pic of exactly what I was imagining in that riser stem. £7 from
CRC, although I'd use an LBS to get their opinions and possibly to try some alternatives before buying.