Is there a straightforward method to find the Kraus operators of a given quantum channel?

you can use the choi isomorphisme:

you apply the Choi map to your channel to obtain the corresponding Choi matrix and then you compute the spectral decomposition of this matrix. The Kraus operators will be the eigenvectors rearranged (vectorization) into a matrix and the weight of each Kraus operator will be the corresponding eigenvalue.