TP+Fly vs. TP:

                        TP+Fly   TP
Catch a Flier           0:48
Route 207 Candy                  0:13
                                 0:05
Flag Solaceon           0:09
Flag Veilstone          0:09
Fight Abigail           0:55     0:30*  (*S+Q tweak timing)
Teach Fly               0:07
Extra Veilstone         0:43
                        4:30            (TP there + get Fly + fight Maylene)
Valor->Verity           0:22     0:54
Verity->Jubilife        0:19     0:27
Iron Island->Mt Coronet	0:29     1:15
Snowpoint->Valor tweak	0:40     2:25
             ------------------------
                        9:11     5:49

Conclusion : TP alone still 3:30ish faster, w/ 6 extra spinner passes compared to Fly+TP