Many places offer flexible working arrangements after a minimum qualifying time - so depending on how bad you want the job, you may need to commit to FT work before you are in a position to negotiate.

Be honest about being interested in flexible arrangements if they ask you directly, but I wouldn't advertise it in the interview unless it comes up. But you need to think about this and be prepared, because if you're not and you're sitting there feeling conflicted, this will show up in your body language and (if they're good) they will know something isn't quite right.