Both players are going to Burton Albion on loan, with the deals running until January 2.
The 22-year-old pair will be at the League One side so they can get first team experience, as they are not close to the first team right now.
Burton are hoping to bounce back into the Championship this season. And they believe the loans will help give them more quality.
Hesketh is a young winger, while Flanagan is a midfielder who can also operate at right back.
Speaking about the deals, Burton boss Nigel Clough said to Sky Sports: "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/forward.
"Southampton have been great and want to see them both get first-team football. They are caught between first team and U23 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."
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