An equal first half was followed by a second 45 in which the Saddlers turned on the style, before eventually finding two late goals.
For Flynn, he was pleased to see Walsall grind out the result and see their quality pay off.
He said: "In the first half it took us a while to get going. I know I made a lot of changes, but we gave Swindon too much time and space.
"There were one or two not sure what to do out of possession, so it's a learning curve for me and them.
"But I was pleased we stuck with it. Swindon didn't really create anything and in the second half I thought we were brilliant."
Despite playing with a back five in the league, Flynn switched to a back four in the first half against Swindon before returning to the back five for the second 45.
When asked if the formation change was notable, Flynn added: "Not really, no, because formations don't win you football matches.
"It's about players knowing when to press, when not to press, when to keep the shape, when to keep the ball and turn the opposition.
"When we did that in the first half we got into some good positions, but we didn't do it enough.
"We slowly grew into it and I thought we were by far the better team in the second half."