Rules As Intended (RAI) - Standing up costs movement equal to 1/2 your highest speed
Jeremy Crawford has put out an official clarification which says:
The rule on standing up from prone fails to account for you having multiple speeds. Here's the intent: if you have multiple speeds and stand up, expend an amount of movement equal to half your highest speed.
This seems like a logical and reasonable way to approach this. If you have 30' walk speed and 60' fly speed, the maximum distance you can move in one turn is 60'. You can split the proportion of walk/fly in many ways, but the end result will be 60' of movement or less. When looked at this way, a character's speed can be thought of as being effectively equal to the maximum type of speed they have.
Thus, it makes sense then that one would simply expend movement equal to 1/2 of that maximum speed (the character's effective speed) when standing up from prone.
So, in OP's example, upon standing up they would have 0 feet of walking and 30 feet of flying movement left.
You would subtract 30 from both because it is consistent with the way that using movement when you have multiple speeds works. If one had used 30' of either walking movement normally then switched to fly one would have the same result (0' walk/30' fly remaining). Same if you started with flying and switched to walking.
RAI vs RAW
Since this is a (now officially acknowledged) hole in the rules, if your table does not care about designer intent and instead wishes to follow the rules as they seem to have been written you can use the logic below. I think it makes a compelling argument that can be made to interpret the rules in the context only of what is written (not taking intent into account).
However, I, personally, do like to follow designer intent whenever possible especially if neither option has a significantly different impact on how much fun the game is (and especially if the RAI are more fun).
Following that logic below leads to a very similar end result as the RAI. In many cases they end up being the same amount of speed remaining, but the proportions of the speed leftover may differ.
Rules As Written (RAW) - Standing up costs movement equal to half of all of your speeds
One way to justify the rules from a purely RAW standpoint is as follows. Since this is clearly a rules hole, arguments could be made for other readings.
Prone's description says:
You can drop prone without using any of your speed. Standing up takes more effort; doing so costs an amount of movement equal to half your speed. For example, if your speed is 30 feet, you must spend 15 feet of movement to stand up.
Jeremy Crawford has said:
Bonuses/penalties to speed apply to your speeds in general, unless the text specifies walking, flying, etc.
Thus standing up from prone would cost movement equal to half all of your speeds.
Additional evidence can be found in the description of grappling
When the game says "speed" without any other qualifiers they are referring to your speeds in general.
Take the case of grappling as further evidence for the fact that "speed" refers to all of your speeds. The grappled condition says:
A grappled creature's speed becomes 0, and it can't benefit from any bonus to its speed.
Clearly the intent here is to say the creature (outside of any extraordinary abilities) does not have any speed and cannot move as a result. If you assume speed here means only one speed, then a creature with a walk and fly speed would be able to fly away with no issues ignoring the grapple completely. This doesn't make sense, and it is clearly not the intent.
Luckily, Jeremy Crawford has once again clarified and again supports this reading here:
The grappled condition reduces any speed you have to 0. If you have a flying speed, it's now 0, and you fall unless you're hovering.
So clearly, when the game says speed they are referring to all of your speeds.
Thus "an amount of movement equal to half your speed" is also referring to all of your speeds.
Thus, even other ruling reaffirm the above interpretation: standing up from prone would cost movement equal to half all of your speeds.
There are even other areas where this same use of speed occurs. See Does Longstrider apply to other speeds? and How do Boots of Speed affect other movement rates? for just two other examples.
In your specific example you would have 15 feet of walking and 30 feet of flying movement left after standing.
After standing up you could then walk 15 feet and fly 15 feet or you could just fly 30 feet (or some division between the two).
The math works out as well: before standing up (with 30' walking/60' flying) you had an effective maximum movement of 60' (since using multiple movements means that essentially you are capped at your largest speed). After standing up (15'/30') you have an effective maximum movement of 30', so half of the original.