No we don’t. This is by and large a New-Age narcissistic notion that leads to the opposite of love. If we would have to love ourselves to love others, there would be no selfless love, altruistic love, transcendental love, unconditional love, pre-personal love, or love from animals. Most feelings of love are created by hormones or when we have our material, sexual, psychological and spiritual needs met by other people. They don’t need to love themselves to trigger feelings of love inside of us. We can even feel loved by people who we don’t know, and have no idea if they love themselves or not.
However, if we define love as the absence of fear, then we can argue that if we are afraid of ourselves, for example by having trust issues, fear of rejection, an inability to be vulnerable, or experiencing ongoing shame and guilt etc., then we need to overcome these fears in order to freely give and receive love. If we call this learning, healing, growing, and awakening to overcome our fears to learn to love ourselves (which in the end is a question of semantics), then by all means, learn to love yourself. Just be careful not to become a narcissist.