Good question, I've often wondered that too.
If the railway tracks that ran below were in a cutting with sloped sides, it might have been possible, but from what I can tell, it is more or less a vertical drop now. Not sure about in 1888 though. Here is a Google Streetview snap from the road in front of the murder site.
If I remember correctly, one of the residents of Buck's Row mentioned hearing a goods train at around the time of the murder. Are you thinking that the killer escaped by performing a death defying leap into a handy open box car full of hay or soft furnishings as the train passed underneath?
The Echo 6 Sept (from the Press Report here on Casebook click )
"It has been ascertained that on the morning of the date of the murder a goods train passed on the East London Railway at about half-past three - the 3.7 out from New-cross - which was probably the time when Mary Ann Nicholls was either killed or placed in Buck's-row."
'Whitechapel' is at Buck's Row on the map. So 'out from New-cross' means the train was heading north to "Shoreditch."
Were there any short cuts from Winthrop Street to Bucks Row.They ran parallel until merging.The witness Mulshaw was reported as night watching premises in Winthrop Street,and only about thirty yards,in a direct line,from the murder scene of Nichols.He reported he heard nothing.