Red hair dye turned my hair pink?

Flame is very brown/orange, it would work diluted over a too-pink red to make it more of a dark red, but the pics the OP added are very pink based reds, so adding more brown/orange may not be a good idea for her. Candy Apple Red or one of the darker Adore reds would be a better choice

Yeah I think Flame would be good if you wanted a warmer or more neutral - or more natural red over a too pink base, but all those photos are what I'd think of as a more purple toned red - when I used Candy Apple I used to call it my blackcurrant cordial hair as it was a really pink/purple toned deep red (not at all what I wanted at the time - but a very nice colour anyway!)