In the 1840 edition, the his modifying people was changed to the, perhaps unintentionally. The 1908 RLDS edition restored the correct his to the RLDS text. In the earliest text (here the original manuscript), we have two instances of his in this conjoined predicate: “and had headed his people in his flight”. This reading is rather awkward, and there is a natural tendency to misread the his in his flight as referring to Teancum rather than Morionton. The 1840 removal of the first his may have been influenced by this difficulty, although even then the his modifying flight could still be misread as referring to Teancum.
One possible conjecture here is that the second his is an error for their; in other words, the original text read as follows: “they were met by Teancum who had slain Morionton and had headed his people in their flight”. If this conjecture is correct, one could argue that during the dictation of the text the original their was accidentally replaced by his under the influence of the preceding his in his people. We have evidence for similar errors in the manuscripts. For instance, in Alma 44, Oliver Cowdery initially wrote his in 𝓞 under the influence of the preceding singular Moroni:
In the following case, an original their may have been replaced by his under the influence of the singular Ammon:
But other evidence suggests that the his in Mosiah 21:29 may be correct (for discussion, see under that passage).
Elsewhere in the text (unlike here in Alma 51:29), the noun flight always refers to the flight of a whole group, never to just its leader. In the following, I list the cases where in theory the text could have referred to the flight of the leader rather than to the flight of his people:
Note that the example in Alma 50:33 refers specifically to the flight of the people of Morionton, not to the flight of Morionton, their leader. So for Alma 51:29 there is some evidence, both internal and external, to support the conjecture “and had headed his people in their flight”.
On the other hand, there are cases where the leader acts for the entire group, especially with respect to military actions. For instance, in the following passage Zerahemnah’s assessment of the military situation also applies to Zerahemnah’s men:
For several other examples of this kind of usage, see under Alma 43:53. Also consider the following case where his tents actually refers to the tents of Moroni and his men:
(Also note that in this example Amalickiah actually refers to Amalickiah and his men, not just Amalickiah.) Under Alma 46:31, I provide a list of several other cases where his tents means ‘their tents’. Thus the occurrence of his flight in Alma 51:29 is not impossible.
Alison Coutts also points out (personal communication) that the verb flee can explicitly refer to a leader fleeing but with the understanding that his men are fleeing with him, as in the following examples (note especially the plural pronoun them in the first example):
In Alma 51:29, the critical text will therefore retain the earliest extant reading, the uniquely occurring his flight (even though this may be an error for their flight).
Summary: Maintain in Alma 51:29 both instances of his, the reading in 𝓞: “they were met by Teancum who had slain Morionton and had headed his people in his flight”; nonetheless, there is some possibility that the second his is an error for their.