I've recently found an open source game engine for Flash and I wondered, is it frowned upon to use an engine like this to produce a game?

What I mean is, what I lack in programming skills, can that be made up for by making good use of an engine already available?

Use of game engines is completely up to the user (programmer).  There are some amazingly advanced concepts out there that you would never be able to learn to do on your own at the earlier (and even later) stages of learning programming concepts.  Personally, I would say if you have a game idea and you absolutely cannot do it without the aid of a game engine, go ahead and do it.  But there are two things that I believe should keep you from using a game engine.  1) Make sure that you're also programming parts of the game, not just editing the engine code a bit and calling it your own game.  You wouldn't learn anything that way.  2) If you have even the slightest belief that you could create the engine on your own, go ahead and challenge yourself. See if you can make it.  You'll learn more that way (even if you fail).

Using an engine is perfectly acceptable. If you look at AG, there are for instance a lot of games that use Box2D - which gives you physics in Flash.

The thing -in my opinion- to keep in mind with using engines is that it adds extra functionality. Now that's great, and usually why you use the engine in the first place, but that also means more things you can configure. Sure, you could create a somewhat okay game without changing many settings, but if you want to make an exceptional game you'll have to check and learn how to use the engine to it's fullest.

Just think, much like BlueJayy said, if you can create this on your own with a little research, you shouldn't get it. On the other hand, if it's more along the lines of 'this will give me what I want and will save me an enormous amount of work', you should get it.

That is exactly it, it will save me an enormous amount of work and I was thinking it would give me more time and energy to concentrate on the content, story and characters of the game.

It'l be my first game, so I'm not expecting it to be fantastic or hugely popular. The engine is purely to allow me to explore what is possible, I'll no doubt learn from the code of the engine itself and be able to develop. Maybe even come up with a half decent game one day.