Hello! When we speak about "accompanying" it means when something goes with something else or to be present or occur at the same time as something else. For example; "The two sisters were to accompany us to London." or "The illness is often accompanied by nausea." And in your sentence; "Accompanied/Accompanying with the increase of private vehicles and expansion of logistics industry, the amount of discharged emissions and waste packing materials is surging." you are saying that "the amount of discharged emissions and waste packing materials is surging." because of "the increase of private vehicles and expansion of logistics industry". So I would suggest that you replace "Accompanied/Accompanying" with "Because of...". Like this: "Because of the increase of private vehicles and expansion of logistics industry, the amount of discharged emissions and waste packing materials is surging." "Because" is a great conjunction to use when there are things happening due to something else happening. I hope that helps!

I feel like “accompanying with the” is more grammatically correct than accompanied in this case. If you wanted you use accompanied instead, then you can word it as “accompanied by the”.