I'm certainly no expert, but the original registration allocation books are lodged with KCC Archives at Maidstone. On their website titled 'Registers of Motor Vehicles' they have this information:
'Registration marks for the period 1903 to 1932 were allocated in the sequence D, KT, KN, KE, KK, KL, KM, KO, KP, KR and KJ. Generally, numbers are shown consecutively within the series but, on occasion, an earlier number is repeated - probably as the result of an owner paying a fee to retain a registration mark'.
'With the introduction of three letter registration marks in 1933, a more standardised procedure was adopted. The series of registration marks allocated to the Kent County Council Licences Department were used in the alphabetical order KE; KJ; KK; KL; KM; KN; KO; KP; KR; and KT. These pairs of letters formed the second and third letters of the three-letter series and were preceded by the letters A,B,C,D,E,F,G,H,J,K,L,M,N,O,P,R,S,T,U,V,W,X and Y. Thus the initial series were AKE, AKJ, AKK, AKL, AKM, AKN, AKO, AKP, AKR, AKT, BKE, BKK, etc'.This would suggest the date for the bike registration would fall towards the late 1920s - early 1930s. A trip to the KCC Archives might be more fruitful?