Clues as to the best method for enhancing grassland with wildflowers can be found in what you've already got. If the sward is herb-rich – it might contain ribwort plantain or cat's ear, yarrow or selfheal – then altering the cutting regime will give these plants a chance to flower and set seed.
However, if coarse grasses dominate and you need to make some space for wildflowers, then yellow rattle Rhinanthus minor is the best plant for the job! It is semi-parasitic, weakening vigorous grasses and opening up the sward to give more delicate broad-leaved species an opportunity to germinate and compete.