In other words, if I started the turn with an empty hand and drew 3 cards because of the No-Hand Bonus, and then I play Inflation, do I draw another card?
A: No. While everything happens immediately in Fluxx, things don’t happen retroactively. The action of the No-Hand Bonus only triggers at the start of your turn, therefore it doesn’t give you an extra card when Inflation is played during your turn. Inflation WOULD affect the current Draw Rule, but that’s not considered a retroactive effect, since the Draw Rule says you must “have drawn X cards on your turn” which is a status for your entire turn, from the beginning. By contrast, the No-Hand Bonus occurs specifically BEFORE the regular draw for your turn, and does NOT count as part of your draw.
Note that Mathematical In Adventure Time Fluxx is an analogue of Inflation, but that Adventure Time Fluxx does not have No-Hand Bonus.
Math Fluxx, on the other hand, has both the No-Hand Bonus as well as Increment All (an Inflation analogue which only applies to Actions and New Rules).