At their best a session IPA is a low gravity APA. At their worst they are watery, overly bitter American blonde ales. So I guess the question is which end of that spectrum do you want to brew?
My go to style is super hoppy APAs Vermont Style - I’m not a huge fan of too much crystal malt but I love 15-20% flaked oats in session IPA’s. I usually use Marris Otter or Pale Ale Malt for base, keep the bitterness relatively low at around 30ibus, add about ½ oz/gallon of 170f steeped hops (I’ve went much higher but don’t like the taste as much without the malt to back it up), and then hit it with 1+oz/gallon of dry hops.
The two brewers I love that produce that style are Tired Hands & Hill Farmstead and rumour has it both use London Ale III - I’ve been meaning to try that fermented cold but have been using Conan (ECY29 Northeast Ale/The Yeast Bay Vermont Ale) or S04/S05 lately.
I have never used flaked oats in a beer. Anyone can corroborate?
I cannot corroborate that you’ve never used flaked oats in a beer.
That being said, they contribute body and mouthfeel without increasing fermentables or changing flavor significantly.
Here is some info on Firestone Walker’s which is one of my favs. It looks to incorporate a lot of the malts mentioned on this thread…
style
Session IPA
abv
4.5%
ibu
45-50
color
4-5SRM
fermentation
100% Stainless
malts
American Pale Malt, Munich Malt, Malted Wheat, English Carmel-35, Cara Pils, Rolled Oats
hops
Bavarian Mandarina, Hallertau Melon, Blend of New Zealand, American Mosaic
Yea, it adds a creamy/silky sort of mouthfeel, body, and definitely a haze.
Living close to Tired Hands and having made the pilgrimage to Hill Farmstead has me hooked on that whole Vermont Style Pale Ale. While it’s definitely a cousin of the West Coast session IPA the main differences seem to be softer mouthfeel (usually a more balanced water approach where Cl is seen as important is S04), noticeable haze, dry hopped like a double IPA but low IBUS, and the yeast derived character.
I think the real key is Munich malt. I like 50 2row, 35 Munich, 10 carapils, 5 c20
To me, the best example of the style is Founders All-Day IPA. Most others seem too thin and watery to me. I’ve never cloned it, but I’ve heard that they have a rather complex malt bill. I’m guessing that there’s a little bit of everything mentioned here - crystal, Munich, wheat, maybe some Rye.
How about I use MO, crystal, Munich, wheat, rye and oats (flakes) and stir in some London Ale III? 8)
I have to admit that I’ve never found those affects from flaked oats.
I’m not sure whether I want oats in my beer. I already have to eat oat bran for breakfast every morning. 
How about London Ale III? I have indeed read somewhere that Hill Farmstead uses it. Would anyone recommend it over London Ale I and Denny’s Favorite?