I feel like this is the cop out answer...but I think that screaming is just part of it all. If I could think of a way to entirely be rid of screaming I am certain I could win some award - a Nobel Peace Prize perhaps!
But, I think that there are some things you could probably do to help.
"Use your words" - This is a favorite phrase of mine. I think that little ones that are starting to use words forget to use them entirely when they are frustrated so they fall back on their infantile way to deal with needs - crying. So, sometimes, calmly saying, "Use your words," can actually really help.
Let him help you - It might take twice as long to cook dinner, but if you get him out his own bowl and spoon and entreat him to help you with dinner it can help. I know that my three year old is a permanent helper now (he's been sitting on the counter so long, he now knows it is his roll, so he comes running into the kitchen at the sound of a mixer - to help).
Talk, Non-Stop - I think it goes against most of our nature to just talk and talk and talk. But, when you are cooking dinner and your hands are full, your mouth is probably not (except for occasional tasty morsels). So, I would narrate what you are doing - give your own little cooking show for your child. Help him decide which lettuce you should use for the salad. Tell him that you are chopping up an orange carrot. Tell him what is happening, but also use it as a time for imagination. If your child likes trucks, or balls, talk about those things. Say things like, "It is a good thing the garbage truck isn't in our kitchen because he may smash these carrots and then we couldn't eat them...you know, the strange stuff that kids like to hear.
Painting: Acceptance by Cezanne