You can sell your luxury items directly from your base in State of Decay 2. This is a fast way to gain influence, especially if you have stocked luxury items and other stuff you just don’t need.
Before you can sell items from your base, you need a couple things to be in place. First off, promote a trader to leader in your community. Check their description in the community menu to see which member will become traders.
With a trader as your community leader, find a large slot outside and build a trader depot. This facility will give you +200 influence each day and most importantly lets you call in other traders of any kind directly to your camp. You can now sell everything from your supply locker without having to travel across the map to a trader.
You can also increase your influence by upgrading your command post to level 3. This unlocks the satellite broadcast which gives you +20% influence gained for 46 minutes.