I have had some experience with wood fired ovens and maybe able to answer some of the problems people may be having with cracking clay and not reaching the required temperature.
Clay ovens are going to crack unless you have a large proportion of sharp sand in the mix, 30-40%, and you need to give it a long time to dry out and fire it slowly at first. Better to make your oven with old broken roof tiles on edge. You should not have a chimney, at least not within the oven, a chimney if fitted is outside the oven door simply to keep the smoke out of your eyes. A chimney within the oven will simply suck the heat out unless you constantly maintain the fire inside or as in some designs a fire under the oven, but this is all an unnecessary complication unless you building a commercial bakery.
When you start firing the roof will be black with soot from the previous burn, this as it gets hot will glow red but then it needs to go white before it is hot enough for baking to start. If it doesn't get this hot you need more wood, or if it never reaches that temperature your oven is too thin or needs insulating. With small ovens, you will probably need to re-fire the oven between batches, so you might prefer not to sweep out all cinders before baking, but leave some pushed to the back to help start the fire again next time.
You need to use small timbers, a faggot of twigs is ideal to start with, but otherwise small well seasoned timber.