I personally disagree with the choice of reds... Not because it's not helping your clear time (because it clearly is the set of red that will help the most your clear time) just because you are compromising your teamfight capabilities. I'd go with magic pen reds (or maybe even hybrid pen).
Starting items : Hunter's Talisman + 3 health pots.
(I don't think the flask is a good investment on Gragas because he already have natural sustain and his later clears are just dumb quick with Runic Echoes)
Something to keep in mind with gragas is that he's now really good at clearing camps AoE wise becasue of his new W. Blue buff start will always be better on gragas because he's not an AS champion to proc the krug stun often. So keeping this in mind...
If you want "the best route" to level 3, you should go :
Blue side start : Gromp (with leash and smite) -> Blue -> Red (smite)
Red side start : Krugs (with leash and smite) -> Red -> Blue (smite)
If you want "the best route" to level 4, you should go :
Blue side start : Gromp (with leash and smite) -> Blue -> wolves -> raptors -> Red (smite)
Red side start : Krugs (with leash and smite) -> Red -> raptors -> wolves -> Blue (smite)
If you don't plan on ganking at all during your first clear maybe doing the "last" camp before the last buff and smiting it for the buff could be an idea... Not sure since I'm not doing it usually.
Usually, I don't do a full level 4 clear, I try to maximize as much my health so I can gank early enough. So my personal first clear looks something like :
Blue side start : Gromp (with leash and smite it) -> Blue -> raptors -> Red (smite)
Red side start : Krugs (with leash and smite it) -> Red -> raptors -> Blue (smite)
Don't forget also that Gragas has a good Scuttle crab clear because of his Body Slam CC. (CC reduces the armor and MR of the scuttle crab) Not that this is something that should matter because it is extremely slow to do scuttle crab for the amount of XP it gives. (But you should still do it for map control and help you regen since it doesn't retaliate and gives you HP back)