While graphene shows a characteristic conical dispersion with a vanishing density of states (DOS) near the Fermi energy E$_F$, it has been suggested that under extremely-high doping ($sim$ 1/4), the extended flat band can be shifted to near E$_F$, resulting in a diverging DOS with strong many-body interactions and electronic instabilities. Although such highly-doped graphene has attracted tremendous research interests, so far the experimental demonstration of doping-induced flat band as well as its associated intriguing phenomena remains rather limited. Here, we report the observation of an extended flat band around the M point in a Li-intercalated graphene, in which the Li ions not only dope graphene with a high electron concentration, but also induce a Kekule order which breaks the chiral symmetry. At such high electron doping, pronounced electron-phonon and electron-electron interactions are clearly identified by the notable kinks in the band dispersion and a strong reduction of the band width. Moreover, by following the evolution of the band structure upon Li intercalation, we find that the flat band and the Kekule order, with the characteristic flat band near M and folded Dirac cones near $Gamma$ respectively, emerge simultaneously, which indicates that they are strongly coupled. Our work identifies Li-intercalated graphene as a fertile platform for investigating the unique physics of the extended flat band, strong many-body interactions as well as the Kekule order.