Running away from the tomb in the final scene is certainly in keeping with Friar Laurence's character. He has just committed an outrageous deception in convincing Juliet to fake her death. He is very afraid of the consequences once the Prince or Friar Laurence's parishioners learn about his deception. He tries to get Juliet to leave the tomb with him so that he can hide her safely in a nunnery, but when she will not leave with him, he runs when he hears the authorities approaching.
We know that his fears and his running away are in keeping with his character because they relate to a philosophy of his that he divulges in the soliloquy he delivers when we first meet him Act 2, Scene 3. In this solilquy Friar Laurence states:
Virtue itself turns vice, being misapplied,
And vice sometime's by action dignified. (II.iii.21-22)
In other words, the things you do that are true and good can actually be turned into immoral actions if your motives are impure or if by human error you mess up in performing your virtuous action. Hence, what is virtuous can also be turned into a vice. Also, Friar Laurence is arguing that questionable acts, or vices can be seen as beneficial if the motive justifies the action.
We have clearly seen Friar Laurence muddle up virtue and vice all throughout the play and now he is running from the consequences of his choices. One way in which we see Friar Laurence muddle up virtue and vice is that he decides to marry Romeo and Juliet that day, in secret, because he believes that it will help end the family feud. While this act is virtuous in that it is well-intended, it is, sadly, poorly thought out and therefore, due to his own human error, becomes a vice. While marrying the couple might have put an end to the feud, agreeing to marry them in secret was not beneficial. Had Friar Laurence waited until the couple's intentions had been made public, the couple's lives might have been spared. We also see him muddle up virtue and vice when he decides to fake Juliet's death. He knows perfectly well that this act of deception is immoral, but since it will save both himself and Juliet from creating greater sins, such as suicide or polygamy, he believes that his motive is justifying his nonvirtuous act. When his plan goes awry, he becomes frightened and does as any man would do--he runs from the consequences. Although, also characteristic of Friar Laurence, he returns, facing the consequences, and explains the whole story to Prince Escalus who declares him to be still "a holy man" (V.iii.281).
Hence, we see that running from his vice is characteristic of Friar Laurence in that it is typical for any man to run from his consequences, but it is also characteristic because his actions leading up to this point have very clearly demonstrated his own philosophy concerning virtue and vice and have all become vices when he intended them to be virtuous.