So far, I understand that type means something like a line or a point but what does this notation mean?: type(x) such that x is an element of F? Or what does type(x) in general mean?
For flags, I have that they are defined as pairwise incident elements of some set. But what exactly is a chamber, my book says a chamber has order I, but what does that mean(to have order I, how can I tell)? What is the order of I? There is also a theorem that says the order of type(F), where F means flag, is equal to the order of F. Order as in cardinnality.
Looking up keywords from your question in Google Books, I found Foundations of Incidence Geometry by Johannes Ueberberg.
This means that $x$ (e.g. a point or a line, in higher dimensions perhaps even more alternatives) is an element of some set $F$ (which I guess stands for “flag”) and you are talking about its type, i.e. you want to know whether this particular $x$ is a point or a line.
Take for example the square with corners $A,B,C,D$ and edges $a,b,c,d$. Then you'd get $\operatorname{type}(A)=\text{point}$ but $\operatorname{type}(a)=\text{line}$. At least if your set of possible types is $I=\{\text{point},\text{line}\}$, as opposed to $I=\{\text{vertex},\text{edge}\}$, $I=\{0,1\}$ or something else. The actual names don't matter for the definitions, but sure help intuition.
A chamber is a flag where every possible type occurs once. So if you have $I=\{\text{point},\text{line}\}$, then a flag would be a point and a line incident to it. Think about higher dimensions, where you have a polytope consisting of vertices, edges and faces. A chamber is a set consisting of one face, one edge of that face, and vertex of that edge.
Due to the definition of the incidence relation, no flag can contain more than one element of a given type. This is because the elements of a flag must be pairwise incident, and incident elements of the same type must be identical. So $\lvert\operatorname{type}(F)\rvert$ is the number of different types occuring in your flag, while $\lvert F\rvert$ is the number of different elements, but since no two elements can have the same type, these cardinalities must be the same.
So in the characterization of a chamber, as I stated it above, it is equivalent whether you require every type to occur at least once or exactly once.