The best way to do this is to:
a) send traps from your routers to Solarwinds for BGP events
[that depends on your model of routers and persuading your sysadmin to send to the data directly]
b) add rules to the TRAPviewer to TAG traps for BGP backward transition (see idea http://thwack.solarwinds.com/ideas/3023 for the definitions of the BGP backward transition traps that cope with both v1 and v2 type traps -- I happened to use BGP backwards transition as the example of a trap that is common and differs between SNMPv1 and SNMPv2. You will need the rule to cope with both cases; I can't export these to show you how to do this, but it's pretty obvious in the trap receiver how to tap a trap that as a particular trap type.
c) use a custom SQL alert and/or custom SWQL query to identify these types of traps.
WHERE nodeid IN (SELECT nodeid FROM traps WHERE datetime>Dateadd(hour,-1, Sysdatetime()) and tag='IPv6_BGP_FLAP' )
Select Caption,count(T.TrapID) as TrapCount from orion.nodes N inner join Orion.Traps T on T.Nodeid=N.Nodeid where tag='IPV6_BGP_FLAP' and datetime > (getdate()-0.01) group by Caption order by count(*) desc
the out of the box route flap detection works on polling the actual route tables, and on the routers here I've around 12,000 or over 500,000 routes in them, so this isn't terribly helpful for detecting a BGP session resetting (since I can get route flapping without a BGP backwards transition)