Is this "layered" XOR cipher secure? I am aware of the vulnerabilities of simple xor ciphers and recently I came across a block cipher that claims to solve those vulnerabilities.

The cipher goes as follows with both the block and key sizes at 256-bits: the key is separated into chunks of length 1 bit.  Every bit in the plaintext is xored with every key chunk.

For example assume that the first bit of the plaintext is 1. Say that the key is 10100101010010101…
The operation that takes place is:

1 xor 1 = 0
0 xor 0 = 0
0 xor 1 = 1
1 xor 0 = 1
1 xor 0 = 1


This continues until the end of the key and the result becomes the first bit of the ciphertext.

Is this really as secure as advertised?
If not why?
If I understand right, your operation effectively is
$$\forall i:  c_i = p_i \oplus k_0 \oplus k_1 \oplus k_2 \oplus \dots \oplus k_n,$$
whith $c_i$ the ciphertext bits, $p_i$ the plaintext bits, and $k_j$ the key bits.

As $\oplus$ (this is XOR) is associative, this is equivalent to 

$$k^* :=  k_0 \oplus k_1 \oplus k_2 \oplus \dots \oplus k_n,$$
$$\forall i:  c_i = p_i \oplus k^*.$$

Now $k^*$ is either 0 or 1 - in the first case this operation is the identity, in the second case it is simple negation. Neither of those can be considered an encryption, and you effectively have a key space of 2 (= 1 bit).

Whoever told you this either wanted to play a joke with you, or knows nothing of cryptography (or both). Or I misunderstood your presention of the algorithm.