Does using the Console in Don't Starve leave a mark?
Suppose I want to use the console to spawn an item, fix a bug, or do whatever.
Will it leave a "cheater flag" in my save file?
There's no cheater flag or anything like that. Console commands are active by default, suggesting it is up to you. The base game is single player so it's not like you're harming other players, there's not really a limit to what you can do so you should be fine.
Normally using console commands or other cheat codes in a game would disable achievements or trophies but there are none in this game so that's not a concern.