21-year-old midfielder Glynn, who signed in 2018 from FC United of Manchester, makes the move to Southport having made four appearances in 2018-19 and spending time on loan at Chorley.
Defender Askew, also 21, heads across to Tameside to join Curzon Ashton for 2019-20 in their Motorama National League North campaign. He made five appearances in cup competitions last season as well as having a couple of loan moves away from Salford.
James Jones, 20, returns to Chester for 2019-20 having signed for us in 2018 after leaving The Seals. He made four cup appearances last season and also spent time on loan with Boston United and Ashton United.