Whether you run into problems within several generations, or not, depends on the genetics of your particular chickens. If they carry deleterious recessives then inbreeding will bring them to the fore. Is that bad? Maybe, maybe not -- it does have the advantage that by SEEING which chickens carry the problem genes, you can remove them from your breeding program and ideally clean those traits out of the gene pool.
If there is not much in the way of hidden 'bad' recessive traits in your particular chickens' gene pool, then nothing particularly bad will come from inbreeding, other than an *eventual* decline in vigor and/or fertility. Emphasis on EVENTUAL. And if it starts occurring, it is easily fixed by bringing in a little outside blood e.g. a new roo.
People fuss too much about inbreeding, if you ask me. Most of the objections seem to have more to do with a human 'oooh, ick, incest!' reaction than actual practical problems. Inbreeding ad infinitum is not good, but used INTELLIGENTLY it can be beneficial (and is sometimes *necessary*) to your breeding goals; and used without any particular intelligent plan but for not too many generations at once, it doesn't generally get you into too much trouble and if trouble *does* show up it is quite easily fixed.
Pat