So Im using axioms from,Frege propositional calculus and is there any way to derive Law of non contradiction as theorem from them.
The axioms
A → (B → A) | THEN-1
(A → (B → C)) → ((A → B) → (A → C)) | THEN-2
(A → (B → C)) → (B → (A → C)) | THEN-3
(A → B) → (¬B → ¬A) | FRG-1
¬¬A → A | FRG-2
A → ¬¬A | FRG-3
And one inference rule, MP
I am not sure what you would regard as an expresion of the Law of Non-COntradiction (would be good to add to your post!), but Wikipedia states the Law of Contradiction as $\neg (P \land \neg P)$
As is, that statement cannot be derived from Frege's axioms, simply because Frege's system does not work with conjunctions... it only uses $\neg$'s and $\to$'s.
So, we could try and state the Law of Non-contradiction using $\neg$'s and $\to$'s by using certain elementary equivalences from Classical Logic.
For example, if we use the classical logic equivalence that $P \to Q \Leftrightarrow \neg (P \land \neg Q)$, then $\neg (P \land \neg P)$ could be written simply as $P \to P$ .. which is a theorem you can derive from Aixoms THEN-1 and THEN-2 fairly easily (most texts on axiom systems will have this proof ... it appears on the second page of this document)
But we can also use $\neg (P \to Q) \Leftrightarrow P \land \neg Q$, in which case we get that $\neg (P \land \neg P)$ becomes $\neg \neg (P \to P)$. Well, we already know that you can get $P \to P$ from THEN-1 and THEN-2, so using FRG-3 you'll then get $\neg \neg (P \to P)$.
FInally, we can say that $\neg(P \land Q) \Leftrightarrow \neg P \lor \neg Q$, and that $P \to Q \Leftrightarrow \neg P \lor Q$. So with that: $\neg(P \land \neg P) \Leftrightarrow \neg P \lor \neg \neg P \Leftrightarrow P \to \neg \neg P$ .. which simply is FRG-3.
This third suggestion is Noah's suggestion from Comments, and it would be my preferred choice as well: it says “if you have $P$, then you cannot (also) have $\neg P$ … which really seems to capture the spirit of the Law of Non-Contradiction, unlike $P \to P$, or $\neg \neg (P \to P)$.
And what about FRG-2, which is $\neg \neg P \to P$? Well, it is saying “if you don’t have $\neg P$, then at least you still have $P$”. In other words, this formula nicely captures the Law of Excluded Middle idea that at least one of $P$ and $\neg P$ is true, which we normally capture using $P \lor \neg P$. But that idea, as the Wikipedia page points out, isn’t quite the idea of the Law of Non-Contradiction … the Law of Non-Contrsdiction says that at most one of them is true, i.e. that they are not both true. For that $P \to \neg \neg P$ seems to fit the bill just right.