Can I synthesize iron acetate like this?
Red iron oxide, Fe2O3, from a paint or art supply store, or as polishing rouge (no additives).  dissolve in aqueous acetic acid, filter off any solids, and go on from there.

Dissolving iron in acetic acid will give you Fe(II)acetate.  Air or peroxide oxidation may (probably will) give you Fenton chemistry and muck up your organics.