Target your arrow images via media queries for smaller screen. For eg. To target screens less than 480px, You can do something like this:
@media only screen and (max-width: 480px) {
.flex-direction-nav .flex-next,
.flex-direction-nav .flex-prev {
-webkit-background-size:50%;
-moz-background-size:50%;
background-size:50%;
background-position: 50% 50%;
}
}
By using background-size
property, you can resize your arrow images. I have made it 50% smaller. You can play with that values to fit your own taste and satisfaction.