The Staffordshire-based outfit have endured a slow start to the campaign in League One, but Nigel Clough has managed to boost his squad with the additions of the Saints pair.
Midfielder Hesketh has made four appearances in the first team at St Mary's, while injuries have restricted full-back Flannigan to just one outing in the Football League Trophy.
Clough told the club's official website: "Jake Flannigan is a young right back who has had injury problems but is now ready for some first team football. Jake Hesketh is a highly-rated midfielder and forward.
"Southampton have been great and want to see them both get first team football. They are caught between first team and Under-23 football at the moment, and just being involved in training with the first team will bring them on.
"They are two good additions to the squad who will fit in well with the youngsters we have got."
Both players could feature when Burton host AFC Wimbledon on Saturday afternoon.