Transposing using suffix notation

let $C= A^{T}A$
Then;
$[C]_{i j} = [A^{T}]_{ik}[A]_{kj} = [A]_{ki}[A]_{kj}$
(where i've swapped the order of the ik on the first A)

now I want to find C transpose. The only way I can think of doing it using suffix notation is to swap the position of the i and j

$[C^{T}]_{i j}= [C]_{j i} = [A]_{kj}[A]_{ki}$

this gives the correct answer but i'm not sure if i'm being inconsistent as first time i swapped order on the same matrix of ik and the second time I swapped i with j- is it because i'm applying a transpose to both matrices at once the second time? if thats the answer though, how do you go about proving that it is the right way to transpose a product using suffix notation (because thats what i'm essentially trying to prove already!).

I don't see the issue. You're doing different things in each case. In the first you're transposing A so you switch i and k. In the second you're transposing C so you switch i and j. You're not assuming anything about how products transpose.

To show that the product transposes the way it does:

Suppose
$C = AB$

Then
$[C^T]_{i j} = [C]_{j i} = [A]_{j k} [b]_{k i} = [A^T]_{k j} [B^T]_{i k} = [B^T]_{i k} [A^T]_{k j}$

ie
$C^T = B^T A^T$

My issue was understanding the difference between swapping i and j and swapping the order of the subscript indices.

i and j are the subscript indices. So swapping i and j and swapping the subscript indices are the same thing.