"I would like to pay tribute to the work that John has done and the faith that he has shown in me and my judgement."
Flynn was appointed by Toshack six years ago with the brief of supplementing the senior squad with young talent to replace ageing internationals.
He has been in charge of Wales' Under-17, 19 and 21 sides since 2004.
Flynn went on to transform a Wales Under-21 side that failed to win a game in 26 attempts between March 1997 and October 2002.
They narrowly missed out on the 2009 European Under-21 Championships - losing to eventual runners-up England in a two-leg play-off.
And despite topping their pool for virtually the whole of the campaign, Wales' Under-21 side narrowly missed out on a play-off place for the 2011 Championships after a 1-0 defeat in Italy on Tuesday.
Flynn has also helped bring through the likes of Gareth Bale, Aaron Ramsey and Jack Collison.
The ex-Swansea and Wrexham boss was interviewed for the Wales manager's job - the third time he has been interviewed for the post - that Toshack got when Mark Hughes left to manage Premier League side Blackburn Rovers in 2004.
But after missing out, he was handed the role of finding and coaching youngsters and worked with assistants former Wales striker Curtis and ex-Manchester United and Norwich City youth coach Williams, who managed Wales for one game on a trial basis in March 1988 in a 2-1 defeat against Yugoslavia, who will continue to work alongside.
Goalkeeping coach Paul Jones remains in the senior setup, but there is no place for Toshack's former assistants Roy Evans and Dean Saunders.
Born: 12 October, 1955 in Port Talbot
Clubs managed: Wrexham, Swansea City
Clubs played for: Burnley, Leeds United, Burnley, Cardiff City, Doncaster Rovers, Bury, Doncaster Rovers, Wrexham
Wales honours: 66 caps (7 goals)
Did you know? Flynn's 12 years at Wrexham makes him one of the longest serving managers in recent history
The Football Association of Wales wants to find a permanent replacement for 61-year-old Toshack who spent six years in charge of Wales.
And after the Switzerland clash on 12 October, they will have five months to decide whether to confirm Flynn permanently in the post - assuming he wants the job full-time - or appoint someone else.
But Stoke City boss Tony Pulis has backed Flynn's claims for the job.
"I'd give it to Brian Flynn," said Welshman Pulis, who had already said the vacancy is "too early" in his own managerial career.
"I think Brian has brought a lot of the young players through that John has used. As an interim manager, to give the selectors a bit of time to choose someone, then I would let Brian get on with it.
Flynn has unearthed and developed the youngsters that former Wales captain Gary Speed has hailed as "the most talented team for 10 years".
Manchester United winger Ryan Giggs, Millwall manager Kenny Jackett and new Sheffield United chief Gary Speed have ruled themselves out of the job.
Former Wales striker John Hartson, who has the Uefa Pro licence badges despite having no managerial experience, revealed he applied for the job.
Ex-Fulham manager and Wales defender Chris Coleman also declared an interest in the post, while Saunders, who is in charge of Wrexham, refused to talk about the position.
Flynn, who won 66 caps between 1975 and 1984, starred the last time Wales qualified for a major finals when the Welsh reached the 1976 European Championships quarter-finals, losing over two legs to Yugoslavia.
He managed Wrexham for 12 years and inspired the Welsh club to one of the greatest shocks in FA Cup in history as they beat reigning league champions Arsenal 2-1 in the third round in January 1992.
Flynn guided Wrexham to Division Two promotion and to the FA Cup quarter-finals in 1997 before leaving in October 2001.
Flynn was named Swansea City manager in September 2002 and helped them beat the drop from the Football League on the final day of that season, before leaving midway through the 2003-04 campaign.
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