I'm going to write the MSc thesis on flight-to-liquidity phenomenon in stock markets and I'm interested in liquidity measures other than Amihud or bid-ask spread.
What are some other popular measures of liquidity?
There are several. This list is from Giyenko et al (2008)---in their work they compare all these different measures--- and includes spread proxies and price impact proxies. As for spread proxies:
Some of these can be interpreted and modified to proxy for price impact. Indeed, any model of price impact is closely linked with liquidity.
From a Macro and theoretical perspective, Tirole has something good to say (as always)
If I remember correctly it established a simple link between the common intuition that Repos, leverage ratios, and other borrowing measures bear relevance to the problem of measuring illiquidity.
Specifically on flight to quality (theoretical, but with an empirical application):