This is a difficult one, because what determines if the Friar can be viewed as trying to gain the glory himself is subtext: that is the way lines are delivered, with body language, tone and presentation. Having said that, we can find textual evidence that suggests that the Friar is contemplating the way in which his actions can bring about the reconciliation of the Capulets and the Montagues, and the way that this will bring glory to himself through his speech in Act III scene 3 when he counsels Romeo after he has killed Tybalt. Note what he says to him:
Where thou shalt live till we can find a time
To blaze your marriage, reconcile your friends,
Beg pardon of the prince, and call thee back.
Note the way in which Friar Lawrence takes this task upon himself. He effectively distances Romeo from the plan, as he will be banished in Mantua, according to the Prince's instructions, and uses the pronoun "we" to refer to his own efforts and others to bring about a reconciliation. Arguably this is taking too much of the responsibility for bringing about a reconciliation onto his own shoulders.