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To be honest when I fit new flooring I always take the skirting off. I have a irrational hatred of scotia beading
Is the flooring a lap joint or tongue and groove?
If it's a lap joint I'd slather the already fitted side with plenty of good quality waterproof PVA titebond III or similar. If you can get hold of it stuff called Alcolin Professional is a aliphatic resin wood glue which has superior creep resistance so the joint is less likely to fail over time due to movement. Once you've slathered on the glue leave plenty of weight on the join to ensure a good bond.
If it's tongue and groove then rip off the bottom "flap" on the groove and repeat the glue process outlined above. It may be worth ripping a small fillet piece to place under the tongue just in case.
Looks to be a good job.
On the bright side it will speed up now......... Until you get to the scribing in the other side that is.