Ive been able to lose attacking escorts by increasing spead during dc runs. However, Im pretty sure that on a few occasions I have alerted them to my presense as well. I dont think there is any concrete timetable here. Such as, you will be safe for "x" amount of time after a dc attack. Its been my experience that sometimes it works and sometimes it dont.
Generally I try to avoid going to flank spead unless Im REALLY in trouble. Seems to me every time I have done that I might as well be shouting through a bull horn "HERE I AM"
When being dc'ed I will go silent run at 1 kt and only increase speed if the dcs are getting close. I tend to use the speed bursts to make quick alterations in my depth or course when the cans are going off then go quiet again as soon as they stop. Once I get a bit of distance, say, 1000m I will risk going to 2kts.
You also have to keep in mind that, depending on the number of DDs attacking you, you may not be able to get away with much. With one DD, you can make all kinds of noise for a short time after it makes its run since you will be in his baffles for a bit. With two or more they tend to take turns listening for you while their mates attack.
Yer best bet is to go silent, go deep and only use short speed burtst while the explosions are going off. Avoid going to flank unless the cans are falling right on yer head.