Does the divorce of prohibition take effect if it was merely a thought or a doubt in its wording, and does it take effect if one went to the street out of necessity then roamed in it with the intention of flirting?

As long as you are not certain that you uttered the oath, then no divorce, prohibition, or expiation for breaking an oath results from it. This is because divorce and prohibition do not occur merely by intention without utterance. Indulging in whispers (waswas) leads to evil and tribulation, and ignoring them is the best remedy.