You may want to consider a high solids no clean. I know this sounds a
contradiction - normally no clean is thought to be synonymous with low residue.
The idea/advantage?
Concerns for flux ander BGA are SIR and solder balls.
An appropriate high solids no clean flux paste or solder paste will 
1) Usually give a non critical, therefore higher yield, joining process
2) tend to plug the gap under the BGA with an inert residue giving high SIR and
preventing ingress of moisture etc.
2) Isolate any solderballs that may have formed 
If you would like  details of  a US supplier of Specially developed BGA
soldering products come back to me.

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To: [log in to unmask]
From: Chris Byrne <[log in to unmask]>
Subject: BGA Flux Cleaning and Testing