What are methods of measuring kcat of an enzyme in vivo? Can we measure the enzyme's fluorescence to determine its kcat? If so, how can we achieve that?
You simply can't. Determination of kcat supposes you control the concentration of enzyme to which you provide a saturating concentration of substrate... The measurement of initial velocity implies you work in a homogenous mixture.
You may do so by quantity of protein. You may do so by speed of the protein. Yes, by the methods above. May change the conversions by U. Yes, you may by fluorescence. And it is by reaction.
Above all, try an enzyme EMIT? MTIA? I would say they have similar names...