It's not that I think the giving of gifts or the lack of giving of gifts is a red flag necessarily. It's all about the kinds of gifts.
In one particular relationship, the man I was seeing told me within the first few weeks (when I was talking about how much I loved the flowers etc around) that he would never purchase me flowers because they just die and therefore are a waste of money. I was shocked and didn't respond but every fiber of my being wanted to scream, "YOU AREN'T BUYING THEM FOR YOU... YOU ARE BUYING THEM FOR ME, AM I NOT WORTH IT?" I couldn't believe that regardless of my likes or dislikes, his frugality and opinions came first. Selfish. And yet I continued to see and fall in love with this man. Who on our first Valentine's together, called me and said, "I hope you don't celebrate Valentine's Day because I don't. It's just a Hallmark holiday anyway." Again, I was shocked but blinded by stupidity and love and I readily agreed to appease him. For our second Valentine's Day together I had told him that it mattered to me, that I wanted to know how he felt. I stood up for myself and he sent me a food bouquet because at least I could share that with people and it was useful, unlike flowers. The gift was a double-edged sword. I was so happy that he acknowledged my need to be acknowledged but hurt because he cared little about my happiness in the gift, it still came down to his needs and wants. This is also the same man that forgot my birthday and bought heartwarming things like electronics etc. But to be fair, he was generous in a lot of ways and I think he gave what he would have wanted to get for the most part (he scored big though when he got me a new Bible that was a study edition because he saw how I took notes in my old tattered one... that was a great gift that was about me and helping me to continue doing what I loved to do).
I'm not saying that gifts are what makes or breaks a relationship, but sometimes listening can. Only one of my boyfriends ever gave me flowers but it was because he got them from a florist (they were the broken stems from the palace in the country I lived in, made into arrangements so they wouldn't go to waste... not especially for me). I've had more than one guy tell me that flowers are a waste of their money (hm... really, but what about the joy they give your girlfriend? What about the smile on her face when she gets them? Not worth it?). I've even told men that I need to feel appreciated by the occasional flower or card or words (words are a gift too), to no avail. That's where the red flag comes in.
When you are in a relationship, you aren't seeking your own happiness and agenda, you are trying to see the significant other happy and to build a joint agenda for life. If the woman loves flowers, give her some once in a while. Let her know that her happiness is worth the $10 for a bundle of grocery store blooms. I promise that the returns will far outweigh the cost of a few flowers that will eventually die.
Be selfless in your relationships but when the other person is selfish (and it can be seen so clearly and simply in gift giving), then see the red flag and wave your white one. Get out of there!