What indication is there at this point that in Myrtle's mind anyway Tom has been more than a fling?

Myrtle's desire for a more permanent commitment from Tom, as evidenced by her repeated mentions of Daisy and her insistence on him taking her to the city suggest that she sees their relationship as more than a fling. Her jealousy and frustration when Tom rejects her requests show that she views the relationship as having greater significance than just a casual affair.