I don't like to carry flat repair kit or tools in my jersey. Stuff I actually use while riding goes in the jersey pockets: snacks, asthma inhaler, phone, bandanna, etc. Tools go on the bike.
Lezyne Road Caddy. Very small and discreet. By far the best value in a minimalist saddle bag. It's what I use on my carbon fiber bikes. Everything I need, no extras: tube, lever, patch kit, CO2 kit, multi-tool. I had to shop carefully to choose those bits to fit properly: Conti Race 28 Light tube (only latex would be thinner), CO2 valve, etc., all had to be smaller than usual. But everything works. I've fixed one flat of my own, and another for a friend, using my kit. Everything works. And I clip a mini-pump onto the frame water bottle cage (Topeak Race Rocket HP).
And I use a Serfas Speed Bag, small, on my old steel road bike. It's bigger than I need but not too big or heavy. Typical small wedge bag, but better made and organized than most. Nifty little pockets, key clip, etc. That bike is already fairly heavy so the bag doesn't add much weight.
Lezyne Road Caddy under my saddle. Flat, secure, weighs little. Photo taken the moment I pulled over to fix a flat -- so far the one and only flat on that bike in a few thousand miles. I hit a chunk of cinder block and got a snakebite flat.