The book pretty much hands us this symbol: the Red Bull on a green field is the design on the late Kimball O'Hara, Sr.'s regimental flag. The woman who looks after Kim (sort of—she mostly lets him run wild) gets confused by Kim, Sr.'s opium-fueled ramblings, and she assumes that the Red Bull is a mystical sign that can help Kim. But no, for once Kim, Sr. speaks literally: if Kim needs help, he should go to Kim, Sr.'s regiment. And eventually, Kim does.
There is one more thing we want to say about the Red Bull, though. When Kim first slips into the regimental camp, he sees all of the officers toasting a little golden statue of a Red Bull. They are all a bit drunk, and this bull statue is clearly a kind of mascot. It symbolizes the unity and importance of the Irish Mavericks regiment to its soldiers. The novel presents this whole scene from Kim's point of view:
The Sahibs prayed to their God; for in the centre of the mess-table—its sole ornament when they were on the line of march—stood a golden bull fashioned from oldtime loot of the Summer Palace at Pekin—a red-gold bull with lowered head, ramping upon a field of Irish Green. (5.55)
By showing this toast through Kim's perspective, Kipling takes something that would have seemed very familiar to his audience—a portrayal of British army bonding—and makes it weird. Kipling shows that it's not just the Indians in the book who have strange social rituals and practices; the British absolutely do, too. Yes, Kim's misunderstanding of this golden statue as the British soldiers's god is supposed to be funny—it shows how unfamiliar Kim is with the British culture he is about to join—but it also indicates that we all have cultural practices and rituals that may seem totally normal when we do them, but that might seem truly bizarre to an outsider (like cow-tipping).