I was wondering if inbreeding is something I should avoid with my chickens?
We are not going to try to raise new chicks for a while now but when we do will we have to get a new rooster every year so that there is no inbreeding?
If you bred everything back to a single rooster, it would still take 8 generations or so, before this would be an issue. The old boy likely isn't likely going to last that long.
Seriously, no. You've enough diversity with a half dozen hens to not be concerned. Line breeding is father over daughter. (It is normal to avoid brother/sister match ups.) Line breeding is extremely common.