The convention is that your weapon icon is called ICON_<ItemBPName> and loaded into the same directory as your item blueprint.
The icons should be 512x256 resolution, and Compression Settings should be set to UserInterface2D. Texture Group (in Level Of Detail section) should be set to UI.
No program or method is officially endorsed by BlackFoot Studios, but here are some icon creation methods suggested by modders:
First set the model up in stager, then change the background color to R:0 G:255 B:0, so it’s easy to go into Photoshop and magic erase the green screen for the transparent png image.
Then apply a B&W filter over the picture and add the Brightness/Contrast filter and just change the brightness to 100 or thereabouts, so it looks similar to the other weapon icons.
You could use Blender, Photopea or other programs for setting up the model.
It is also possible just to screenshot the item inside the Mod Kit editor, but you might want to apply some post-processing similar to what is described above.
Another option, which may not create the best icons but which will allow your icon to be relatively consistent with other icons, is the Item Photo Booth, located within the ItemPhotoBooth map in GBCore/Maps. Just follow the instructions and it will create a passable icon within the My Documents*/GroundBranch folder (* or whatever your local equivalent is).