My mornings were like this too I hated being the shouty Mum every morning too and it drove me to distraction, so I had to do something about it.
First of all we pack bags when we finish homework the night before and at the same time I sign any letter-slips, which go in their bags there and then and also write any notes or letters for their teachers, which also go straight into their bags. We then write a list of any unusual/extra things to remember for the morning (eg money for collections, stuff for special lessons) and put it all together ready in a specific place. (I find this bit is essential at this time of year, with all the run up to Christmas activities and nativity stuff etc.)
We also typed up a list of what everyone needs on each day and stuck it on the front door. Its only small (A6 size) so fairly unobtrusive, but it means we can stop and check everyone has what they need before we leave the house.
We put them each a peg up on the wall specifically for their coats and school bags and a basket in the hall for school shoes. This means they can always find everything in the morning.
Mine are also terrible for losing hats, gloves etc. So I bought a job lot of plain black magic gloves off ebay and some plain black hats and we keep them all together, so everyone can just grab a pair of gloves and a hat in the morning. If the basket starts looking low in numbers I make a mental note and either ask them in the morning to check at school (which they inevitably forget to do) or remind them when I go to collect them and send them back in to do it then.
They have to get up when I tell them to (7.30 am) but are allowed ten minutes on the sofa with a blanket to wake up slowly before I start pressurising them to get ready. This has really helped, as it just makes them stressed and grumpy if they have to get going straight away.
We tend to stick to a fairly strict routine as far as getting ready goes. So its, toilet, breakfast and drink, vitamins, wash/shower, get dressed, hair brushed.
They usually have at least 20-30 minutes left over to read, play or do whatever else they want. Then ten minutes before we have to go out, they put on their shoes, coat/hat/gloves and pick up their bags, while I get dd (22 months) togged up and into her pushchair.
Then we check off the list we made the night before and the one on the front door, grab any extra bags we need and off we go.
We have much less stressful mornings these days and I now have time to make their lunches up as well as cook their porridge, because they know what they are doing and in what order, and have had time to wake up properly before they have to start.
I did used to make their lunches up the night before, but I prefer to do it the same day if I can so its fresher.
The other thing that helps is being organised at the other end of the day. So we do a mini version in reverse when we get home from the school run. Shoes in basket, coat and bag on peg, upstairs to get changed, toilet, snack, homework, pack bags, write list and the rest of the afternoon/evening is free time.
I'd say it probably took a couple of weeks to 'train' them into the habits, but it was well worth the effort. The boys soon realised it was worth their while as well, because they now get time to play or read before school instead of it all being rush, rush, rush.
Before we started doing all this, we did used to have 'getting dressed races' where dh would time them on his watch to see who could get dressed the fastest and they used to love seeing if they could beat their fastest times.