How do I memorize hand signals faster being called out as a play during football?

Make a video of each hand signal and draw the play associated with each hand signal. My school's football team also does a lot of hand signals and this helped me out. Also I don't know if your coach does this, but my coach's hand signals can be related to the plays. For example, one play we run is called "Paper" and my coach's hand signal is opening a book. Another play we run is "Flex" and the hand signal is a bicep flex.

I played as a WR in college, and now coach the QBs. What works best for me is to get a list of the play calls, and write down what the hand signals are for each part of the play. Then go through the list of plays and give the signals to yourself in front of a mirror as if you are the coach. By teaching yourself to call them you are also teaching yourself to recognize them. This worked great for me (even though we have over 100 signals), hope it works for you! (If you aren't near a mirror you can just do it without one.)

They sell blank flash cards, with rings to hold them together, on Amazon. Maybe you would find it helpful to put the hand signals on this type of flash card. I find it a good way to stay organized when I need to memorize a lot on a specific topic.