I have a large flat brown mole on my breast, it hasn't changed but I've thought about getting it checked how would it be removed since on my breast?

The exact same way . As it would be removed from any body area. If it's sufficiently suspicious to indicate biopsy, it should be removed in its entirety, but, since it's on your breast, only by an abps- certified plastic surgeon. Recently, the consensus is that shave biopsy is adequate & leaves a slightly depressed, hypo pigmented scar that can be subsequently revised, but excision with sutures is isually preferable.
Signs of Melanoma. There are certain signs specified by american cancer society called abcd to look for early detection of a concerning lesion. Asymmetry, border irregularities, colour variability, diameter more than 6 mm. If those signs are present then lesion should be biopsied. Any growing lesion with personal or family history of melanoma should be checked by a surgeon or a dermatolgist.