Hello Bob, glad to see that you have an interest in making engines, but you might want to save a flame eater as a more advanced project. I have not built one myself, but I've heard that they can be quite finicky. They require a very good fit of the parts if you ever wish to see it run.
The best place to start is with a simple steam engine built from bar stock. Wobbler style engines are the easiest to build. After you have done one of them, you can try something a bit more complicated, such as a mill engine that has an eccentric and a slide valve. I highly recommend building a number of bar stock steam engines before you try your hand at an IC engine. By doing so you will learn many things that will be important as you get into more complicated things. Once you feel you have mastered the lowly steam engine, try your hand at a popular but easy to build IC engine known as a 'Webster'.
Now, in order to build some engines, you will need some plans to work from. A great place for free steam engine plans is
http://www.john-tom.com/ Once you are there, you will want to take a few minutes to find your way around, but you want to end up in the steam engine area for 'Elmer's Engines'. Elmer Verburg was a model engine enthusiast and designed many engines from very easy to build, all the way up to some that were more complex. Look through his plans and you should have no trouble finding an engine or two to get yourself started.
If you go into the IC engines portion of the john-tom site, plans for the Webster engine are there also, listed under "Four stroke petrol engine plans". There are 21 pages in the plans for that engine. It is a simple four stroke engine, but not a hit and miss engine even though it looks somewhat like one. It is a very popular choice for a hobby machinist's first IC engine.
There are other plans out there, some free, some you have to buy. When you feel you are ready to tackle a more complex gas engine, you might want to try a set of plans from the late Jerry Howell. His engine plans are very well done and very popular. We hobbyists are fortunate that when Jerry passed away, his family sought to fulfill Jerry's wishes, and they still offer his plans for sale at this site:
http://www.model-engine-plans.com/ Jerry was a very talented and passionate model engine designer and it shows in his plans.
The sky is the limit when it comes to what you can build. As simple or as complex as you like. You can make engines from bar stock or from castings. With some experience you might even want to try designing an engine of your own. Feel free to ask more questions if you wish, there are plenty of people here that can help you get started.
