Truth or Lie

Either the person who flipped the coin is a truth-teller or he is a liar. Let's start with the first case wherein the person is a truth-teller. If this person is telling the truth, then the coin must be heads by his own statement. He has stated that the coin is heads if he is telling the truth.

However, if this person is a liar, then the biconditional he gave ("The result of the toss is heads if and only if I am telling the truth") is false. The only way a biconditional can be false is due to either (but not both) the antecedent ("I am telling the truth") or the consequent ("The result of the toss is heads") being false. By virtue of this person being the liar, the antecedent must be false. This in turn makes the the consequent true, meaning the coin must be heads.

Regardless of the truth of the given statement, the coin must be heads.

If he is telling the truth it is Heads. If he is lying it is also Heads because if the if and only if part.

"If and only if" is a two way cause-and-effect.
The statement has two possible ways of it happening :

1) toss heads (T) <---> tell truth (T)
==> For him to be able to tell the truth, both parts of the mutual cause and effect must have the SAME truth values.
==> Because telling the truth has to be true, tossing heads must also be true.

OR

2) toss heads (T) <---> tell truth (F)
==> For him to be able to tell lies, both parts of the mutual cause and effect must have OPPOSITE truth values.
==> Because telling the truth has to be false, tossing heads must have been true anyway.

==> Tossing heads is a constant no matter what that person told, whether it's the truth or a lie.