No. He could't transfer his memories to the previous flash even if he wanted to.
The previous flash and the next flash were totally different as seen in the episode. Initially we could see that the flash was travelling in the right (R) as seen from our perspective. But finally when the wormhole was created, we see the new flash come by the left (L), catching up to the original flash (R).
The reason they both saw what happened to be speed mirages (see below) was that when both the flashes saw each other, they were surprised and hence they drifted into parallel universes. The original flash (R) reverted back to his original universe whereas the new flash (with his memories) drifted away from the original universe and made a new universe. Hence the original flash could not get the memories of the previous timeline, because,
- He will never have created the wormhole in the first place
- The new flash was not the same as the original, because of the daily changes he encounters, like cellular changes.
The speed mirages were actually imprints left by each of the flash before being seperated, i.e. both of them actually existed for a moment before being seperated.