Entei has a poor movepool and defensive typing, and is countered by Pokemon used on nearly every team. Additionally, he's nothing special; Suicune and Jirachi are better Substitute + Calm Mind users, and Blaziken and Houndoom are better Fire-types in standard play. Nonetheless, Entei is less fragile than the latter two and can get past Blissey in an unorthodox and sometimes unexpected way.
Entei can actually beat the standard Blissey with this set, as long as the following conditions are fulfilled: Entei has to be at full health, Sand Stream must not be up, and Blissey must switch in as Entei uses Substitute. Set up with Calm Mind while Blissey Seismic Tosses twice to break Entei's Substitute. Alternate between Substitute and Calm Mind until Entei has six Calm Mind boosts, then start frying Blissey. Be sure to keep a Substitute up if possible to protect Entei from status and Dugtrio.
Entei should aim to hit 404 HP, as this lets his Substitutes survive Seismic Toss and Night Shade. With 285 Speed, he beats Medicham, while 296 is enough for all Heracross. 300 lets him outrun Salamence and other neutral-natured base 100 Speed Pokemon, and maximum Speed is viable too.
This can put quite a dent into teams that do not have Blissey or Snorlax and rely on their Water-types, Tyranitar, or Regice to stop Fire-types. Sunny Day lowers the power of Water-type moves while boosting Entei's Fire attacks, and also removes SolarBeam's charge turn. Entei's Special Attack stat is rather low though, so Milotic and Suicune might still be able to stall him out. Calm Mind can help with that, but Hidden Power Ice messes up Salamence and Flygon very nicely. Beware of Tyranitar switching into a SolarBeam, however, as Entei will be forced to stay in and be crushed by Tyranitar's Rock Slide. This moveset is probably better done by Houndoom, who is slightly slower, but has more Special Attack.
401 HP lets Entei survive five Seismic Tosses or Night Shades with Leftovers intact; the magic Speed numbers to consider are as listed on the previous set.
Toxic is a decent move on Fire-types, as Water-types generally hate being poisoned, as do Salamence, Tyranitar, and Gyarados. Reflect supports your team against Snorlax and other physical threats. Roar is iffy on a Pokemon with few good resistances and such low Special Defense; nevertheless, it might be able to mess up Celebi that carry a Grass move instead of Psychic. Psych Up lets Entei steal Calm Mind boosts from others, but the most common Calm Mind user, Suicune, isn't going to care much. It will be priceless if used on a Regice that stole Calm Mind boosts from another of your Pokemon though, and it always works on Celebi.
Entei learns several physical filler moves, such as Body Slam, and has a decent Attack stat as well. However, he should generally stick to special attacking because of his special STAB and access to Calm Mind. You could try a novelty Leer + Hidden Power Fighting set to take down Snorlax, Tyranitar, and Blissey, but don't expect too much of it—even Arcanine will do it better with Howl.
Checks and Counters
First of all, Water-types: Suicune and Milotic don't take much damage from Fire-attacks and can hit back with a STAB super effective Surf, while Swampert can do the same with Earthquake. However, Swampert has to beware of Hidden Power Grass, which OHKOes him after a Calm Mind. Other, lesser used Waters will do fine, but these three are the most common.
In addition, Entei has a lot of trouble with Dragon Dance users. Tyranitar, Salamence, and Gyarados all resist Fire and can hit him hard with Earthquake—or, in Tyranitar's case, Rock Slide. None of these Pokemon are very fond of Toxic though. Finally, Blissey and Snorlax are decent counters. Blissey can wall the Sunnybeam set and sometimes even the SubCM one, while Snorlax has Thick Fat and can hurt Entei with STAB Normal moves or Earthquake.