The point was enough to move the Coasters to the top of the fledgling table on goal difference, although Darlington 1883 could overtake them if they beat Chorley tonight.
Sam Finley gave Flyde a 10th minute lead, but Jordan Hulme pulled the Ammies back on level terms after 27 minutes.
And then on the hour-mark, Michael Nottingham put the visitors ahead.
Seven minutes later, Danny Rowe levelled for the hosts.
However, Mike Phenix looked to have won the game for Salford with a goal in the 85th minute.
But a minutes into stoppage time, summer signing Steve Williams equalised to earn his side a share of the points.