What evidence does the Time Traveller have to prove that what he says is true at the end of The Time Machine?

The one piece of evidence that links the account of the
Time Traveller to reality and clearly shows that his narration is based on truth are the
two flowers that Weena picked for him and which he placed in his pockets. It is the
presence and the reality of these flowers that helps the Time Traveller himself to
belief in the reality of what has happened to him. Note the following
speech:

"To
tell the truth... I hardly believe it myself... And
yet..."

His eye fell with a mute inquire upon the withered
white flowers upon the little table. Then he turned over the hand holding his pipe, and
I saw he was looking at some half-healed scars on his
knuckles.

The flowers are a
tangible piece of the future that the Time Traveller brought back with him, and act as a
symbol of the future and the Time Traveller's feelings for Weena. It is of course
important to note that the medical man himself finds something "odd" in the flowers, and
is unable to recognise or identify them precisely. This adds veracity to the account of
the the Time Traveller, and his refusal to let the medical man take the flowers away
shows his awareness of the danger of letting such future relics be
studied.