Bit late to the party on this one, but I'd make a couple of observations:
1. Andrew's absolutely right that any borrowing which is subsequently invested into BPR qualifying assets no longer provides any IHT relief (the borrowing is set against the BPR assets first). This doesn't apply where the assets are sold, but that invites the CGT problem. The gains could be rolled over into EIS shares, rather than AIM shares, but these tend to be higher risk, so you save 28% CGT and risk losing 100% of the investment.
2. LozaACCS suggested selling the flats and reinvesting into a property development company to claim EIS CGT deferral relief. However, property development is an excluded activity for EIS purposes, so the relief wouldn't apply. As Andrew suggested, taking the cash and creating a trading business qualifying for BPR would also be a challenge.
A further option could be to look at setting up a family trust and gifting up to £650,000 of the properties into trust. This would allow you to hold over the gain (assuming UK trustees) and the 7 year period would start to run. Bearing in mind the age of the parents though this may not be a strong option as they would need to survive for the full 7 years to avoid them being clawed back into the estate, however, from the date of transfer all growth is then out of the estate. Considering the way house prices are moving this could be a considerable saving over 5+ years. Plus there would be a saving of £130,000+ if one parent survives 7 years and £260,000+ if both parents did.
They would, however, have to be excluded from benefiting, which means they would not be able to retain the income or any other benefit. Plus, as mentioned earlier, it's unlikely to be effective if either needs to go into care as the LA would likely look through the trust. Trusts are complex and full advice should be sought.