The (theoretical) arms and armour of the English militia of this period are set out in a 1253 Assize (p.431). As in many such cases, these are ideals and not necessarily adhered to. I shall be doing some other militia as armed peasants. Hopefully Legio Heroica will one day produce some spearmen with gambesons but no mail.
Incidentally, this assize has been cited by the US Congress in support for the right to bear arms.
I based the flag in this source: it dates from the time of King John*. The flag of London, since sometime in the 14th century and before Wat Tyler's rebellion, has been what looks like the cross of St George but with a sword in one corner (as shown here). This is the flag of St Paul**. I really couldn't decide what kind of flag to use. I originally painted it as a banner, which is perhaps more suitable for the description of Fitzwalter carrying it on horseback. I then saw a modern version which is a vexillium type, still used by churches. Since the flag was donated by the cathedral, I thought I'd do this kind. Unfortunately, I prefer the painting I did on the other banner! I think I shall have a third attempt, with this seal as a guide.
Segrave was the step-son of de Somery, a leadiing royalist, and this may have helped his rapid rehabilitation after Evesham. He, and his sons, are mentioned in the Caerlaverock roll. He changed the family arms from the bushels to a crowned lion, though it is unclear when he did so. I have hedged my bets and shown his banner with the older arms and his shield and caparison with the newer version.
*I went to Worcester Cathedral today and while I was there I went to see King John's tomb again. There is also one of the 14th century Beauchamps there.
** Worcester Cathedral is also St Paul's - I didn't know until today that they use the same arms as London.