Here is a team for Pokemon yellow, but they can work in red and blue also.
Pikachu: Starter. May not be able to evolve in yellow, but is the only electric type to get thunderbolt by level up (but only in yellow) Very fast, and gets good coverage. in red/blue, definitely hunt around in viridian forest for one. Just to let you know, if you use your own Pokemon in stadium, the stat experience pikachu will have by lv 100 (probably even earlier, but you'll probably bring your mons to 100 before doing prime cup) will give him better stats than the rental raichu, so it can still rock in stadium, especially petit cup.
Thunderbolt: Stab, best electric move in the game, with 95 power, 100% (technically 99.6%) acc, and 10% to paralyze. Red and blue pikachu will need to use tm 24, but yellow chu can learn it himself, leaving the tm available for someone else.
Body Slam: Best normal move in the game, with base power 85, 100 acc, and 30% chance to paralyze. need tm 08, from the ss ann
Submission/Surf: Surf is better, but only available after beating stadium, so submission will do. Submission is the most powerful fighting move in the game, with 80 power and acc, but 1/4 recoil. Note that recoil damage is not taken in stadium if the target is ko'd by the move.
Thunderwave: Paralysis is at its finest in gen 1, and is a fate worse than death for fast sweepers like alakazam. 1/4 chance each turn for target to not move is just icing on the cake, as the main point is to cut speed. Thunder could be used if you want another attack instead of status.
Charizard: I'll admit he may be pretty bad in gen 1, but he still has plenty going for him for use in game, namely immunity to ground, excellent moves, and a strong fire move by level up that does not require staying unevolved.
Flamethrower: Stab and very strong
Slash: Learned upon evoling into charizard at lv36. 70 power 100 acc and hi crit (which means always crit in gen 1) makes an attractive choice.
Fly: Hm, only flying stab available (and only in yellow).
Earthquake/Dig: Back in gen 1, dig was basically a two turn earthquake, having the same base power 100. Earthquake is preferred, but dig will do if needed earlier or earthquake required elsewhere.
Nidoqueen: Most people seem to prefer the male counterpart's better offenses, but nidoqueen learns body slam at lv 23 AS a nidoqueen, so you can still use that moonstone right away. Movepool is very wide, so this is just one option.
Body Slam: learned by level up, very strong.
DoubleKick: Very good move, learned at lv 12 in yellow, though learned too late to be useful in red/blue, not due to power, but having to be unevolved for double kick.
Earthquake: Stab, learned only by tm sadly.
RockSlide: Provides perfect neutral coverage with earthquake.
Other options include surf, icebeam/blizzard, thunderbolt/thunder, and more.
Venusaur: Very bulky grass type, eggxecutor is technically better, but it is much harder to find.
Razor leaf: Hi crit plus stab? yes please.
Sleep Powder: Puts opponent to sleep, very good for catching and battling
Leech seed/MegaDrain/Swords Dance: Restore health or boost power of coverage below while foe asleep.
Cut/Double Edge: Need some coverage. Double edge obviously better, but cut is needed, and due to being pre power creep, base power 50 is not as outclassed as it is in later gens.
Gyarados: I recommend this guy over blastoise, as blastoise is outclassed everywhere except defense. In gen 1, gyarados had base 100 special, making special moves still very strong
Surf: Stab hm, best hm in the game, and argueably the best water move of all time. Use bubblebeam or watergun ubtil available
Strength: body slam is better, but already used for pikachu, who can't learn strength, and base 80 power physical move off of base 125 attack hurts alot.
Fireblast,Thunderbolt/Thunder,Blizzard/Ice Beam,Bite: Choose two; thundrbolt better than thunder, but blizzard still has respectable 90% acc. Fireblast Very powerful, with high burn chance. Bite is physical and can flinch.
Flareon: Considered the black sheep (err, fox/dog) of the eeveelutions, flareon is still worth mention, with base 110 special and whopping base 130 attack.
Quick Attack: May seem a strange choice, but flareon's epic attack and pitiful speed make priority viable.
Flamethrower/Fire blast: Flamethrower is learned by level up, albeit very late. So fire blast is an option for immediate power.
Smog/Reflect/Double Edge/FireSpin/Bite: I admit that flareon's movepool sucks, but here are some possibilities. Smog is a poison move with poor accuracy and power, but a nice 40% to poison. Double Edge Hurts Plenty with that high attack, and won't do recoil if the target faints, making it a great finishing move. Bite is only listed for a non recoil option, as flinching won't happen if the target has already moved. FireSpin Is the fire equivilant of wrap, and can be useful if the target is already poisoned, burned, or seeded. Reflect halves damage from physical moves, which helps cover for flareon's low defense and can support teammates
If you want flash, just use a boxed Pokemon and put back afterwards: even cut is better than pre gen iv flash, and that even considers the power creep in later gens.