once you have found a legendary dog it has gotten away from you this is how you can find it again.

1] use your poke'dex and search for where it is.
2] then DO NOT FLY to where it is. walk.
3] the dogs move 1 route at a time. so if u fly more than 1 route away they will jump more than 1 route at a time. so you will never catch it.
4] start walking to where it is.
5] then the dog should walk closer to u so you should en up like this..

......V (you)..........V (a gap / route inbetween)....................V where the dog is.
6] <(*.*)> Route > ......................................=[ (the dog)

7] if you walk into the next route it should come in there aswell.
8] once the dog is in your route check by using a pokedex each route u move.
9] use a max repel
10] then use your radio and use the channel that attraks wild poke'mon and then walk around.
[Note] if you leave the route the dog will go in the opposite dirrection. so dont leave.
[note2] use a poke'mon with mean look or scary face or something that stops your tartget from fleeing poke'mon that have this are.. wobafet and ghastly. so have one of them at the front of your party.
[note3] when you damage a legendary it will stay at that health and wont heal itself so i recomend using paralysing moves so that it is always on.

and yea hopefuly you catch ur pokemon.