When I googled "sir richard francis burton biography" the top result about the biography is this https://burtoniana.org/biography/. It wrote these words interestingly,
The most important archival biography is Mary Lovell's A Rage to Live (1996). Jon Godsall's important biography of Burton, The Tangled Web (2008) is a useful dose of skepticism. Byron Farwell's crisp Burton (1963) is the most balanced and critically detached. Fawn Brodie's The Devil Drives (1967) is still very readable. All biographies of Burton should be read skeptically as many of his biographers tend to accept the stories that surround his life uncritically.
The best seller on amazon about Burton seems to be Rice Edward's Captain Sir Richard Francis Burton: A Biography. But the link said
Highly imaginative but dubious. Sold well, but seems to have used an interpolation technique to deduce 'facts'.
So far I have read Byron Farwell's "Burton: A Biography of Sir Richard Francis Burton" (one of reasons is the link says it is the most balanced and critically detached)
So can someone recommend any other books? I also find that all these books don't get enough ratings on amazon, even Rice Edward's book only gets 87 ratings.
BTW, English is my second language so Mary Lovell's A Rage to Live, which has 910 pages is quite a challenge for me. I would like to pass that one.