Unironically, I think Books are a good request here. Not for the "haha Mathilde likes books" joke, just straight up.
Kislev is already going to be straining, and Boris will have many, many other demands on his attention and limited political capital. Asking him to shield Vlag as a favor (ie to an extent beyond which such cooperation would naturally benefit Kislev) is unfair to both him and to Vlag, when we both know that he must put his own people first.
However, as a conflicting requirement, we want to request something which can seem totally above-board and plausible for the Tsar to push for - if we request that he do something blatantly favouring Mathilde Weber and/or the Grey Order and/or the Empire in an uncharacteristic way after his father died, then suspicions might get raised.
But books are something we can request. The costs to him are relatively low, and indeed it's easy to see how such an arrangement could be outright net beneficial to Kislev if they are able to preserve more critical knowledge through the next Chaos incursion, so it can be sold on that level.
The major reason that such arrangements wouldn't already be on the table is that it's still a major pain in the ass that also reduces Kislev's bargaining position on the academic front, thus requiring a display of trust that the commitments would be followed through with instead of just jacking Kislev's knowledge and not aiding in the later reconstruction.