How should I improve my chopping flow?
Although this is partially personal preference, in general you should have the uncut ingredients on the side of your non-cutting hand. This will set up a logical flow of material which keeps you from having to reach over your cutting hand.

If you chop with your right then you'd have the uncut ingredients on your left, as after knife work your chopped ingredients will be on the right of the knife. Everything else comes from this. If you are chopping a lot of ingredients it makes sense to have a few bowls handy to put the chopped ingredients into so you can keep your board clear. 

My workflow is based on the assembly line principle - that is do all of one type of task before moving onto another to limit the amount you have to move: before chopping I get bowls for each of the chopped ingredients (stackable stainless steel bowls from a kitchen supply store are great for this as they clean easy and take up little space), and array the bowls to the right of the board. Then I wash all the ingredients, peel them, and prep them at once rather than doing it individually per ingredient and place them to the left of the board, so I have all my ingredients ready to chop. Then I take each type of ingredient and chop them one at a time, saving any messy (tomatoes, cheeses) or possibly contaminating ones (meat, seafood) for last, as I will have to clean the board, my hands, and the knife after possible contaminators to prevent cross-contamination. As the board fills for each ingredient I will transfer the chopped ingredients to the bowls, but I wait until I need the space to continue cutting - if you move the chopped ingredients each time you finish chopping one of them then you waste time moving your arms and body around. 

This is the fastest way I have found to get a lot of ingredients processed. If you wash, prep, peel, chop and move each ingredient individually you spend a lot of extra time moving around the kitchen.